TIME AND RATIONALITY

Jean-Pierre Dupuy

	France's Nobel Prize in economics, Maurice Allais, under whom I was lucky enough to study, used to say: "When it comes to rationality, the fundamental maxim is: only the future matters."  Obviously he did not mean that the past is not important.  In a certain way, the past makes us what we are: if the past had been different, we would be different and, in particular, when faced with a given problem, we would certainly not make the same decision.  No, what Allais's maxim asserts is that the past will always be what it was and, specifically, our present decision cannot change it.  This metaphysical principle of the fixity of the past with respect to free action is what underlies Allais's maxim.  What could be more obvious or less controversial?  When I compare a number of possible actions, I consider only the impact their foreseeable consequences will have on me, the others and the world.  This word must be taken in its etymological sense: that which accompanies the action but occurs after it.  Whether I do this or that might have an effect on the future of the world, but certainly not on its past.  Thus, rational choice theory is sometimes called a consequentialism.

	Again we seem to be in the domain of the obvious.  Moreover, violating Allais's maxim truly seems to lead to characteristic irrationalities, of which we will soon see several examples.  However, the nut of my argument is that this maxim cannot be universally valid.  I will, of course, be talking in terms of reason and not of psychology.  Most of us break Allais's principle in a good many minor, everyday decisions.  We also break it when we are faced with choices concerning the way we most deeply define ourselves; or even our "salvation," or whatever takes its place.  Rational Choice Theory (like Philosophy of Mind, to which I will often resort in the following analyses) has always been uneasy when faced with what it holds to be irrational and which is a paradox or challenge for it.  However, here we will not be concerned with the actual practices of agents, but with what those practices should be.

	I will begin by examining several cases of violation of Allais's principle which, it seems, it should be uncontroversial to consider irrational.  I will establish a certain progression which will lead us to a rupture: suddenly, the diagnosis will no longer be taken for granted, and we will have to ask why.

1.	Irrationalities

	1.1.	Suppose I notice that a certain private club is very highly rated by my friends and acquaintances.  Many people are ready to incur non-negligible costs of all kinds in order to be admitted.  From this I infer that admission to the club is an extremely desirable goal.  I set it for myself and strive hard to achieve it.

	Is it irrational for me to believe that admission to the club is a goal which merits being pursued?  Would my behavior be irrational if I accepted to pay a high price to be admitted?

	Not necessarily.  We are dealing here with an unobservable, quasi-metaphysical entity: the value associated with being a member of a closed, exclusive group of people.  When a value is uncertain and difficult to estimate, it can be rational to imitate the behavior of others in their efforts to obtain it.  To be sure this is a heterodox view in the small world of rational choice theorists, where imitation is generally considered to be an element of irrationality.  Rationality implies independent preferences, absence of mutual influences and, more generally, absence of all phenomena associated with crowd or fashion behavior.  However, this excessively incomplete vision of things must be resisted, as Keynes made especially clear in the context of financial markets and speculation.  The argument can be made as follows.  The others may have clues or information to which I have no direct access: by imitating them I can benefit from their knowledge.  Of course they might be just as ignorant as I am, but I know nothing about even that.  I thus lose nothing by assuming they know something.  (A Bayesian argument can be made to support this line of reasoning; see Orléan (1990).)
	1.2.	After deliberation, I decide to pay the price (in the broad sense) of admission - and I am admitted.  What a disappointment!  The members, the ambience, the conversations, the activities all appear to me to be mediocre, ordinary, vulgar.  I have now two sets of evidence available to me - or so it seems.  On the one hand, there is my direct perception that the club is worthless; on the other hand there is the fact that it was expensive to be allowed in.  I place more weight on the latter than on the former and draw the conclusion that the club is not so bad after all.

	I have been influenced here by an article by a cognitive psychologist at Stanford, Amos Tversky, whose work on rationality has hit hard at the rational choice edifice.  It has shown, in effect, that the axioms of the theory are in practice violated massively, universally, and, undoubtably most troubling of all, systematically.  Far from being chaotic or random, these violations seem to obey rules, as if they were subject to what one hesitates to call their own rationality (Quattrone and Tversky, 1987).  I believe that these results must be taken seriously, but on the condition that one go beyond psychological analysis.  Again, the problem is to determine what rationality should be, not what the "implicit" rationality is in practice.  I will thus depart from Tversky's analysis when the time comes.

Let us go back to our club.  Amos Tversky takes a fraternity on an American campus as his example.  I prefer an illustration which is more literary and more Gallic.  Marcel, the narrator of La Recherche made many sacrifices in order to win his heart's desire: to be received in the Guermantes Salon.  He had to wait until Sodome et Gomorrhe to finally be invited.  Once there, however, he found none of his expectations fulfilled.  Yet he resisted the obvious and resorted to this astonishing rationalization: on that particular occasion the salon was not in its normal state because he was there!  The physics of Proust's time was already open to the idea that the observer's presence disturbs the system being observed.

	This is a case of what psychology calls cognitive dissonance between a previous, a priori belief (that the club or salon was desirable) and uncontrovertible evidence (which proves the mediocrity of the object in question).  Rational revision of the belief, which would satisfy Bayes's rule, does not take place.  Why?  Because the subject takes another piece of evidence to be indisputable: the high price paid for admission.

	Yet this is clearly irrational.  The fact that in the past I incurred costs to obtain X should not come into play in the judgment I make as to the desirability of X - in other words, as a reason for me to think that X is desirable.  Or so it seems.  How can this form of irrationality be described?  According to Tversky and Quattrone, we are dealing here with an inversion of the causal link between desirability and cost, or a confusion of causal and diagnostic contingencies. One is ready to pay a high price for X because one believes X to be desirable.  The costs one is thus ready to assume are only the evidence, the manifestation of the desirability which one grants to X.  These costs do not, and should not, play a role in the evaluation of X.

	There is another way to express what appears to us to be irrational in this "behavior" (which is in this case not an action but a mental process).  In the first step, we saw that the fact that others incur or have incurred heavy costs in order to obtain X can reasonably play a role in my evaluation of the desirability of X.  Here we see that the fact that I incurred similar costs should not play a role in this evaluation.  What is the difference between me and the others which explains this asymmetrical treatment?  The others' belief that X is desirable provides me with a reason to believe that X is desirable, but my past belief does not.  My past belief cannot in itself constitute a reason for my present belief if elsewhere I have acquired a good and decisive reason to abandon or revise it.  However, my past belief may be the cause of my present belief if we suppose that the mental process responsible for the evolution of beliefs brings into play auto-reinforcement mechanisms or hysteresis phenomena.  One would then have a case of a mental event (the past belief) causing another mental event (the present belief) without counting as a reason for the latter.

	This is precisely the way in which the American philosopher Donald Davidson characterizes irrationality in general.  Going against many philosophical traditions, Davidson has argued that the reasons we have for acting must be treated as causes of our actions (1980).  However, some mental causes cannot be considered to be reasons: the case we are examining is an example of this.  Under such circumstances, we must speak of irrationality.  Davidson has studied the conditions of possibility of this type of case (1982).  It is significant that his point of departure is the case we examined at the beginning: the influence one mind has on another.  This makes it clear how a mental event (the one which occurs in the subject's head, his belief for example) can be the cause of another mental event (the belief of the imitating subject) without constituting a reason for it.  (I have argued that the belief of the other could under certain circumstances be a reason for my own belief, not that this is always the case.)  The case of many minds is paradigmatic for Davidson.  If there is, in a single mind, a mental cause which is not a reason, we must grant, he concludes, that this mind is separated into relatively closed compartments, after the fashion of Freudian structures.  This argument is not among the most solid, but let us apply it to the case in question nonetheless.  Everything occurs as if my past belief, a cause of but not a reason for my present belief, were isolated from my self, the self that now forms a belief.  I, my present self, imitate my past belief: I use it as a model, as if it were the belief of some one else.

	1.3.	The third step is an irrationality well-known to economists, and often denounced by them.  Maurice Allais likely had it in mind when he formulated his principle.  It is known as the sunk cost fallacy.  In rational choice theory, unlike accounting, all expenses must be considered written-off at the very moment they are incurred.  This is a direct application of Allais's principle.  This time the irrationality of the sunk cost fallacy no longer concerns belief formation, but action itself.  It would be better to say: action in the service of belief.

	I have acquired some expensive equipment.  I judged it rational to make this investment because I thought it probable a certain event would occur.  I was, however, mistaken.  For example, I naïvely believed that television programs would amuse and instruct me, and I acquired a highly "sophisticated" TV.  I have been awakened to my error.  What should I do?  Use the equipment or get rid of it?  In principle, rationality requires that I not take into account the cost of the investment when I make this choice.  This expense is a sunk cost, it will always belong to the past and "only the future matters."  In other words, my decision should be the same as that which would be rational if the equipment had been given to me.  Thus, the costs and benefits of my decision to use the equipment considered as a gift must be compared with the costs and benefits implied by all other options open to me.  I could thus be lead to consider that it would be best to discard the TV, which implies writing off the purchase cost and acknowledging the a posteriori irrationality of the original decision.

	Most of us do not act like this, and the sunk cost fallacy is one thing people everywhere have in common.  This equipment was expensive, so the costs must be recovered.  The more paid for it, the more it seems indispensable to use it, even if doing so is very expensive and provides few returns compared with other options.  We are prodded into acting in this way by a concern for internal coherence between our past and present selves.  This concern must be better analyzed.  According to Allais's principle, we are engaging in perfect irrationality, but we nonetheless feel that there is a kind of logic behind it.  By committing the sunk cost fallacy, I am in fact acting according to the rules of imitation, as in the first two steps.  This time what I am copying or imitating are neither the beliefs or actions of others, nor my own past beliefs as if they belonged to some one else - it is the behavior which would have been mine if the circumstances had been those I was expecting and my decision to make the investment had been a posteriori justified.  In Tversky's terms, this is once again a confusion of a causal issue with a concern for diagnosis.  My action targets not its causal consequences, but the diagnosis which it will allow me to make of the situation.  The TV completely satisfies my needs, the proof is that I am using it right now.  Thus I am now reassured of the coherence of my choices, and of my rationality.

	Things can also be presented in the following way.  My behavior symbolically aims to change the past through imitating what would have been the causal consequences of a different and more desirable past.  On this view, we can see the logic of vengeance in the sunk cost fallacy.  An act of vengeance also aims to change the past.  In fact, it attempts to abolish it by claiming to annul one act of violence by a new one, when all it does is add to the first one.  The sunk cost fallacy consists in adding operating costs to an unjustified investment cost as if this would provide revenge for the latter.

	The logic of the claimed irrationality of the sunk cost fallacy is so strong that certain authors do not shrink from defending it.  Thus, Robert Nozick (1993) resorts to the following illustration.  He likes going to concerts.  He knows that it is good for him and that, anyway, it is better for him than staying home and watching television.  However, he lives in Boston and it is very snowy and cold outside: it is extremely tempting to not go out even though, all things considered, it would be better for him to attend the concert.  We know where the good lies, but we take the opposite direction: since Aristotle, this form of irrationality has been called akrasia or, in modern terms, "weakness of the will."  Nozick has a way to keep himself from giving in: he "ties his hands" by buying season's tickets.  In rational choice theory it is well-known that a number of problems can be given a satisfactory solution if, paradoxically, the actor or actors agree to restrict their margin of manoeuvre ahead of time by "tying" themselves, in one way or another, to something or someone else: by precommitting themselves.  One classical example might be that of Ulysses who had himself tied to the mast in order to escape the sirens (Elster, 1979).  In Rousseau's terms, this means forcing oneself, or agreeing to be forced, to be free.  We will come back to this.  However, has Nozick really tied his hands by buying season's tickets?  The fact that he has already paid for the ticket should in no way count in his decision to go or not, since this decision should be the same as it would have been if he had been given a free ticket.  To think otherwise would be to commit the sunk cost fallacy.  We could thus think that Nozick is attempting to neutralize one irrationality (weakness of the will) with another (the sunk cost fallacy), when all he is doing is adding them together.

	1.4.	The fourth and last step along our way is the class of common cause Newcomb problems.

	Consider the following classic example from the great American statistician R. A. Fisher.  We know that there is a strong correlation between tobacco smoking and lung cancer.  Suppose that it is discovered that the reason for this correlation is not, as was thought until now, that tobacco smoking causes lung cancer.  The cancer is caused by a certain gene which also predisposes people to smoke.  Let's take the case of an individual who enjoys smoking.  Does this person now have a reason to quit?  (As was the case under the interpretation which prevailed until now: smokers were guilty of "weakness of the will.")  Her decision will in no way alter the fact that she has, or does not have, the lethal gene.  It would be irrational for this person to deprive herself of the pleasure she feels, by hypothesis, when she engages in her vice.

	Yet, if this case is made subject to the golden rule of rational choice theory - namely: always act so that you maximize your mathematical expected utility - we must conclude that it is rational to refrain from smoking.  So, if we are convinced (as are most authors) of the contrary, we must explain what is wrong with rational choice theory in its traditional form (which dates from Leonard Savage and John von Neumann).  This question, and the class of problems in which it arises, are at the origin of a schism within the world of rational choice theorists.  The vast majority of authors assert the irrationality of the behavior which, in this example, consists in quitting smoking.  Their argument leads back to Allais's principle: whatever the subject does, her action will not change the past, which, here, means the presence or absence of the gene.  They must thus amend the golden rule in order to make it compatible with their conviction.  A small minority opposes this orthodoxy.  Its members follow the golden rule in its original form and conclude that refraining is rational.  According to the orthodoxy, they are committing a grave mistake.  They reason as if quitting smoking were the price, relatively small compared with what is at stake, that the agent accepts to pay in order to acquire the evidence that she does not have the fatal gene.  This behavior is perfectly irrational, protests the orthodoxy: it consists in taking the evidence for the thing.  It is magical, in the proper sense of the word.

	Fisher's problem is characterized by a double relation between the action (here, the decision to refrain or not) and the state of the world (the presence or the absence of the gene).  There is a (strong) probabilistic dependence between the action and the state of the world although the action is not the cause of the latter.  Any problem presenting this double relation of probabilistic dependence and causal independence is called, by definition, a Newcomb problem.  This configuration is permitted here by the existence of a common cause of the action and the risk of lung cancer.  This is why Fisher's problem is said to belong to the sub-class of Newcomb problems with common causes.  All problems belonging to this class have the following form: a state of the world C causes, at the same time, a very favorable state of things X and a moderately costly decision x:

	For this class of problems, maximization of the expected utility according to the usual procedure - namely, through the intermediary of conditional probabilities (of the states of the world given the action) weighing the outcomes - leads to a decision considered irrational (by the orthodoxy).

	Why is this?  Conditional probabilities are indifferent to the nature of the links they make manifest - indifferent to the fact that these links are or are not causal.  The orthodoxy holds that when I decide between several possible actions, I must consider only the causal consequences of my action and their more or less desirable characteristics.  The more or less desirable character of the state of things manifested by my action, or for which my action would only be evidence, should not be taken into account.  When an agent maximizes his expected utilities in the usual way, he acts as if he had an external vantage point on himself, as if he were someone else.  He discovers his decision in the same way we do and his strategy is to act in such a way as to make the news that this discovery brings as favorable as possible.  The subject reasons that if he does this, then his action will make manifest the presence of such and such desirable features in the world.  I would like this to be the case, thus I act in this way.  The orthodoxy concludes that this is irrational, magical behavior.  Things are even more serious than they seem.  If the action makes manifest the state of the world, that is here because it is caused by it.  In consequence, to act in a given way because what can be inferred from one's action is a favorable diagnosis of the state of the world, which is a state determined in the past, is to give oneself an unimaginable power: the power to choose one's past.  

	Decision theory as reformulated by the orthodoxy is known as the causal decision theory.  It is now clear why this is so.  The traditional theory, to which the minority clings, is rechristened the evidentialist theory.  From the preceding, it is clear that the evidentialists have their work cut out for them if they want to be taken seriously.

	Evidentialism presents features which we have learned, in the earlier stages of our discussion, to associate with irrationality: looking at oneself from the outside as if one were someone else; giving oneself power over the past.  I would, however, like to propose a defence and illustration of evidentialism in what follows.  This does not imply that I wish to do this against the orthodoxy, in other words, the causal theory.  My thesis (Dupuy, 1992) is that rationality is not univocal.  There are two forms of rationality which are irreducible to one another.  Since it puts them into conflict, the class of Newcomb problems has the merit of revealing and identifying them.  These two types of rationality correspond to two different, though inseparable, conceptions of time - better expressed as two authentically human experiences of time.

	Before presenting a whole series of arguments in favor of this thesis, I would like to take up an example with considerable theoretical and historical importance.  The present debate seems unaware that this example is the paradigm case which has inspired, to varying degrees, all the others.  Here I am referring to the famous thesis, in the form of a paradox, advanced by Max Weber, on the "correlations" between the "Protestant ethic," or more precisely the ethical consequences of the doctrine of predestination, and the "spirit of capitalism" (Weber, 1930).  Tversky and Quattrone are an exception.  They address the issue, but unfortunately without referring to Weber's analysis.  This may account for our differences in interpretation.

	Here I will examine only the logical structure of Weber's argument, not its empirical validity.  In virtue of a divine decision taken for all eternity, each person belongs either to the camp of the elect or to that of the damned, without knowing which.  No one can do anything about this decree, and there is nothing anyone can do to earn or merit salvation.  However, divine grace manifests itself through signs.  Here what is important is that these signs cannot be observed through introspection: they are acquired through action.  The principal sign is success obtained through testing one's faith in a worldly profession (Beruf).  This test is costly.  It requires one work continually, methodically, without ever resting secure in, without even enjoying, one's wealth.  "Unwillingness to work," Weber notes, "is symptomatic of the lack of grace. (p. 159)"

	Here we again find the logical structure of a common cause Newcomb problem:

	The "logical consequence" of this practical problem, Weber points out, should "obviously" have been "fatalism."  Here fatalism means the "orthodox" choice, Non-x, the choice of the "dominant" strategy, as it is known in game theory: whatever the state of the world - here, whether I am one of the elect or not - it is better for me to lead a lazy life.  (This "fatalist" choice is equivalent to, in the Fisher problem, continuing to smoke.)  However, Weber's whole book attempts, as we know, to explain why and how "the broad mass of ordinary men" made the opposite choice.  We are perhaps more or less, whether we like it or know it or not, the inheritors of this choice - the evidentialist choice.

	The Calvinist doctrine of the masses held it "to be an absolute duty to consider oneself chosen, and to combat all doubts as temptations of the devil, since lack of self-confidence is the result of insufficient faith, hence of imperfect grace. (p.111)"  The means of acquiring this self-confidence, the means of assuring oneself of one's state of grace, was "intense worldly activity." (p.112)

	The debate between the Lutherans and the Calvinists is extremely interesting.  The former accused the Calvinists of reverting to the dogma of "salvation by works," to the great dismay of the latter, outraged that their doctrine could be identified with what they most scorned: the Catholic doctrine.  This accusation amounted to saying that she who chooses x reasons as if x were the cause of X - magical behavior, insist the accusors, since it consists in taking the evidence for the thing (x for C).  This accusation is no other than the one causal theorists today make against their adversaries, the "evidentialists".  From this we can see that the present debate is more than it claims to be: a defence of rationality, and that it has theological roots.  This should surprise no one who, taking the point of view of the Durkheimian tradition, is convinced that what we call Reason has its origins in religious thought.

	I have just used the expression "as if."  It is ambiguous.  If it is interpreted to mean that the two lines of thought lead to the same result, then the accusation has good grounds since in practice both doctrines, the Calvinist and the Catholic, are indistinguishable - and in an extremely paradoxical way the Calvinist doctrine even reveals itself to be much more meritocratic than the Catholic doctrine (Weber, p. 115-16).  However, if the interpretation is that the Puritans really took the sign to be the thing, the accusation then becomes incomprehensible and completely unjustified.  For Weber shows that, as is well-known, ascetic puritanism constitutes the final stage of the vast movement of "elimination of magic from the world" which rejects "all magical means to salvation as superstition and sin." (p.105)  He emphasizes that this Puritan view is what "stood at the cradle of the modern economic man" (p. 174), "gave birth to economic rationalism" (p. 259, n. 4) and transformed the "calculating spirit" of capitalism "from a mere means to economy into a principle of general conduct." (p.261)

	Of course one could place the derogatory label "irrational" on the Puritan choice - in other words, the evidentialist choice.  However one should be aware of the risks one would be taking.  Economic rationality - it is important to note here that I am referring to the rationality of economic actors, not of economists -represents for many the pinnacle of Reason in history.  Weber's analysis incites us to think that this rationality belongs to evidentialism's camp.  Are we ready to face the paradox of judging it ...irrational?

	1.4.	In order to move ahead in this discussion of the presumed irrationality of evidentialism, I would now like to introduce a new category which has caused much ink to flow in philosophy of mind.  For philosophers of mind, it represents a kind of summum of personal incoherence: self-deception.  Since many Anglo-American philosophers, in spite of their usual aversion for French thought, do not hesitate to cite Sartre, I will use this term in the sense of mauvaise foi as it was used by the author of L'Etre et le néant, in other words, in the sense of lying to oneself.

	Weber dubs the Calvinists "saints overflowing with self-confidence" and "Self-Proclaimed Saints."  The issue I would like to examine now is: did they also deceive themselves, did they lie to themselves?

	Tversky and Quattrone give a positive answer to this - the same response which can be given to any evidentialist choice.  Their argument can be put in the following terms.  Propositions (1) and (2), used in the situation under examination, are both true:

(1)	The Calvinists believe that they have placed themselves among the elect by choosing x;

(2)	The Calvinists believe that they have not placed themselves among the elect.

	(1) and (2) express contradictory beliefs.  Furthermore, one could think that:

* The Calvinists find a way to hide (1) from themselves

* because they want to believe they were chosen by God.

	If we further postulate that the first belief is the cause of the second, without, obviously, constituting a reason for it, we obtain a pure case of self-deception as described by Donald Davidson (1986).  Thinking perhaps of himself, he takes the example of a man preoccupied by growing baldness who manages, using various cosmetic and, especially, psychological means to deny the obvious, but whose efforts have perhaps more successful effects on his own perceptions than they do on those of others.  This man believes that he is bald and believes that he is not bald at the same time.  He manages to hide from himself the fact that he has the first belief because he wants to have only the second.  Yet it is certainly because he has the first belief that a mental mechanism of wishful thinking sets in and leads him to have the second belief.
	I do not want to deny that this is an acceptable interpretation of the evidentialist choice.  At Stanford, Quattrone and Tversky have done a series of impressive experiments in which they place their subjects in situations which have the structure of a common cause Newcomb problem.  The remarkable result is that not only do the great majority of subjects make the evidentialist choice, they deny (to the experimenter and it seems likely to themselves) having intentionally chosen x in order to make a favorable diagnosis about themselves.  I simply want to propose another interpretation which reveals the rationality of the evidentialist choice.

	On my view, the Calvinists can be said to have the following two beliefs, which are not (necessarily) incompatible:

(3)	The Calvinists believe that they did not place themselves among the elect because they believe God chose them;

(4)	The Calvinists believe that they were free to choose x or Not-x when they chose x.

	From the beginning I have been telling essentially the same story, with a few variations: is it worthwhile to pay the price of admission to a very exclusive club?  However, common cause Newcomb problems have one fundamental difference with those mentioned above.  The critical decision is no longer made by the agent: some one or something, God or Nature, has already chosen for him.  My thesis is that this difference weighs heavily in the question of rationality.  Under Tversky's interpretation, proposition (2) is irrational: the Calvinists adopt the belief that they themselves are not responsible for their being among the elect because, in their deepest hearts they know very well that they have acted to give themselves the signs of the elect and they want to hide this truth from themselves.  Under my interpretation, the Calvinists believe that they have not proclaimed themselves saints simply because they take seriously the premises of the problem as they have been submitted to them or as they have internalized them: God has proclaimed them to be this way.  They nonetheless face a formidable problem: they must consider it to be not incoherent to believe both that God has chosen for them (proposition (3)) and that they are free to choose (proposition (4)).

	Certainly, one might object that (4) is not really one of the givens of the problem.  However, what would be the sense in questioning the rationality of the agent if she does not have, or does not give herself, free choice, understood in its minimal sense as the ability to act in a way other than the way in which one does?  In terms rooted in an extremely old philosophical tradition, for an agent to be able to take seriously a common cause Newcomb problem, he must first be convinced that it is reasonable to be "compatibilist:" in other words, to believe in the compatibility of determinism (here, causal) and free will.

	I will now show that there are two ways to defend compatibilism, according to the degree to which determinism menaces free will.  Furthermore, the solution given to the compatibilist problem determines the solution to the Newcomb problem.  The distinction between two forms of rationality and two forms of temporality to which I referred above is thus rooted in the distinction between two conceptions of determinism.

	The following analyses are fairly technical in a way which is not very familiar to rational choice theorists.  They are grounded in today's prolific work in analytic philosophy which reopens the compatibilist question as it was set out by Aristotle and then developed by scholastic philosophy.  The conceptual tools used in this work are taken from various areas of contemporary Anglo-Saxon philosophy: possible worlds theory (which is itself a reappearance, due to D.K.Lewis and R. Stalnaker among others, of Leibniz's philosophy) and counterfactual reasoning; classification of conditionals, a much-debated issue both in philosophy of language and in cognitive psychology; belief-revision, which is studied in epistemology, Artificial Intelligence and also in economics.  I will limit reference to these tools to a strict minimum in order to avoid burdening a discussion which I intend to concentrate on the issue of paradoxes of rational choice insofar as it is situated in time.
2.	Two Temporalities, Two Rationalities

	2.1.	Like all occurrences in the world, actions leave traces, such as memories in the minds of people.  In favorable cases, these traces can be followed back to the events of which they are the reflections, copies or representations.  If this were not possible, disciplines as diverse as archaeology, history and psychoanalysis would be unthinkable.  Generally, less attention is paid to the inverse possibility because our conviction that time flows irreversibly in one direction is so strong.  Yet it can sometimes be legitimate to treat an event which precedes another as the trace in the past of the latter.  Consider an event which occurs at t2 : at t1 _ t2, this event could have been preceded, announced if one likes, by its cause (causal determinism); or it could have been predicted correctly (theological determinism if the predictor is God); or else it could have been true at t1 that the event would occur at t2: "it was written" (logical determinism); and if the event is an action there are yet other possibilities.  The subject could have formed the intention at t1; or this action could have been announced through threats (deterrence) or promises (engagement, contracting).  It is sometimes possible to trace the event occurring at t1 forward to the event occurring at t2.  If the latter is the action of a subject, one can argue that the existence of these traces in the past, or if one prefers, these memories of the future, render the agent incapable of taking any action but the one she took.  This is the classical argument of those who deny free will and who are known as incompatibilists because they assert the incompatibility of determinism (of any sort: causal, theological or logical) and free will.  I will now sketch out the incompatibilist argument in the condensed form which contemporary authors have given it.  I will then examine the possibility or possibilities of refuting it.

	2.2.	Let us call "C" the event which occurs at t1 and "x" the action at t2 which C announces.  "S" designates the subject.  We can write:

A1:		C occurred at t1
A2:		If C occurred at t1, then S does x at t2
Thus A3:	S does x at t2

	We should note the role played by A2: this proposition expresses the temporal chain which links C to x;  it characterizes C as that which announces x.

	The incompatibilist argument applies an operator of necessity which is generically represented by the symbol   .  When this operator is applied to a proposition, it asserts that the proposition is true in all possible worlds.  More specific to our problem, we will call   St the operator of necessity such that:
  St(p) means: p is true and S is not free at t to perform an act such that, if he performed it, p would be false.
	The incompatibilist argument can be written thus:

N1:		 St2 (C occurred at t1)
N2:		 St2 (If C occurred at t1, then S does x at t2)
Thus N3:	 St2 (S does x at t2)

	N1 expresses the principle of the fixity of the past.  At time t2, A1 is necessary, not because it has always been necessary but because it has become so.  It was contingent that it become necessary.  It is "accidentally necessary," according to scholastic terminology.

	N2 expresses the fixity of the temporal link which unites events C and x.  Depending on the case, we could be dealing with the fixity of the laws of nature; or the fact that the predictor is omniscient in all possible worlds; or indeed any other thing, subject to the nature of the temporal link which makes C the announcement of x.  We must note that N2 is equivalent to:

		(5) (C occurs at t1)   (S does x at t2)

in which the symbol   expresses strict implication in logic.  The meaning of (5) is that in all possible worlds in which C occurs at t1, S does x at t2.  It is fundamental to understand that A2 is not sufficient to imply (5).  In truth, this is the point of origin of the bifurcation between the two forms of temporality which we will be lead to distinguish.  A2 is an indicative conditional the validity of which is limited to our world.  A2 does not exclude that in a possible world other than ours, in which C occurs at t1 as in our world, S does not do x at t2.

	The conclusion N3 says that S does in effect do x at t2, as was "announced" at t1, but that S did not act freely because it was not in his power to act other than as he did.

	Can one be compatibilist?  Can the above argument be refuted?  The thesis I am defending is that, depending on the nature of the problem, the agent has two possibilities, neither of which has greater a priori legitimacy than the other.

	a)	The agent could accept N1, in which case he would have to reject N2.  The past is fixed, thus the subject, who considers himself to be free, must give himself the power to invalidate the fixity of the temporal chain which links C to x.  The nature of this power must be made clear.  Obviously, it is not that in our world the subject can act so that the link between C and x will be violated: this would be contrary to hypothesis A2, which indeed remains valid.  Rather, it is that the subject reasons in this way.  Suppose that C took place at t1 and, thus, that I will decide to do x at t2.  While I do perform x at t2, I know that it is in my power to perform Not-x.  It is thus in my power at t2 to do something (in other words, Not-x) such that if I were to do it, the link between C and x would be invalidated.  This is because, since the past is fixed, the fact that C occurred at t1 would remain unchanged.  By acting other than the way I do, I would enter another possible world (since I am free), in which the relation expressed by A2 would not hold.  This power is called counterfactual.

	This option corresponds to the orthodox view.  It rests on Allais's principle: the past is fixed in relation to my present action.  Consequently, "only the future matters."  If, as in the case of common cause Newcomb problems, there is a dominant strategy, it must be chosen, as we have seen.  By convention, we have called "C" the favorable common cause (the absence of the lethal gene in the Fisher problem, or, in Weber's example, being among those chosen by God), and "x" the evidentialist strategy.  Non-x is thus the dominant strategy, and it is endorsed by the orthodoxy.  Since the agent decides to do Not-x and he believes A2 to be valid, he must infer that at t1 Not-C existed, not C.  He must claim that it is rational to continue smoking with the knowledge that this choice proves he has the fatal gene.  The ungodly Calvinist must convince himself it is better to indulge in idleness life even though this choice reveals that he is among the damned!  It is too easy for the evidentialist to reply that if such is the case, she would willingly seem "irrational" if doing so would ensure (or rather assure) her good health or even her eternal salvation.  While it is troubling, this argument is not entirely convincing and I will not use it because I have, I believe, a better one.

		b)	The agent's other option is to accept N2, but then he can only reject N1.  This time the temporal chain A2 is held to be fixed (in other words, as true in all possible worlds).  The agent, considering himself to be free, must thus give himself a counterfactual power to invalidate the past.  Let us examine this:  obviously this is not a causal power over the past, which would be completely inconceivable unless we were writing science (or rather philosophy) fiction.  More reasonably, the agent thinks in the following way.  Suppose that C occurred at t1 and thus that I will decide to do x at t2.  While doing x at t2, I know that it is in my power to do Not-x.  It is thus in my power at t2 to do something (or Not-x) such that if I were to do it C would not have occurred at t1 since the fixed link between the past and my action entails that if C occurred at t1, x is what I would do.  By acting in a way other than the way I do, I would enter another possible world (since I am free), in which the past would be different from what it was in my world.  This is the nature of the power which Alvin Plantinga (1986) named the counterfactual power over the past.

	It can thus be shown that by giving herself this power over the past, the agent in the common cause Newcomb problem is rationally lead to choose x - in other words to make the evidentialist, or Calvinist, choice.  (Dupuy, 1992; the demonstration, however, requires the additional hypothesis that Non-C causes Non-x).

	At this crossroads, we are faced with a meta-decision.  The great majority of professional philosophers who reflect on these problems resolutely take the orthodox path: they unhesitatingly adopt Allais's principle.  In contrast, "the broad mass of ordinary men" (at least in the Californian, therefore strongly Puritan, population in which Tversky performs his experiments) take the other route.  Is this crowd "irrational"?

	At this point it should be clear that two conceptions of time are in opposition.  Their essential difference has to do with the past.  The fixity of the past with respect to our free actions seems to be very much a part of the very essence of what we call rationality.  Allais's principle gets its strength from this intuition.  However, three remarks are pertinent.

		a)	The class of Newcomb problems is responsible for revealing that there is a thorny problem here.  Now, it is certainly not for nothing that in these problems, the past is not known and is unknowable except through signs of various kinds (causal consequences, predictions coming true, etc.) which it leaves in the form of actions performed by free agents.  Is a past which is unknown, and impossible to know directly, fixed to the same degree as a known past?
		b)	Moreover, there is much to say in favor of the fixity of the law or rule which characterizes the evidentialist choice.  We will soon see that it offers a way out of pragmatic paradoxes which commonly occur in life in society.  The risk of "superstitious rule-worship" - i.e. of making the rule, or law, sacred -, promptly denounced by the orthodox camp, certainly does exist.  However, we will see that a similar risk menaces the principle of the fixity of the past.  This principle can also become the object of quasi-religious devotion.  An illustration of this will be provided below.

		c)	One very important result of the preceding analyses is that there is no need to resort to an inconceivable power to change the past, or to choose it, in order to found the evidentialist choice.  There is thus no reason to reproach the Puritans for giving themselves a power, which belongs only to God, to save or damn themselves.  A much more "innocent" power, as the analytic theologian Plantinga (1986) says, suffices: a counterfactual power over the past. 

	Firmly adhering to the principle of the fixity of the past, the orthodox theorists place themselves in what I call the temporality of history or occurring time (Dupuy, 1992).  I call it the temporality of history because, as a discipline, history treats the past as an object and also because, in a certain philosophical tradition, events spring up in history without shedding any light on the past insofar as they are pure beginnings.  In the terminology we are using here, events seen as Ereignisse play no role as evidence.

	I hold that as humans we experience another form of time, which I call the temporality of projects or projected time.  Let us go back to the strict implication (5) which is its characteristic formulation and not shrink from reading it according to the classical metaphor.  It is the inscription in the past of the agent's future free action, (the future contingent).  Everything is already "written."  As Diderot said, "It is like a Great Scroll which is unrolled little by little" (Jacques le Fataliste).  The agent acts according to a previously prepared scenario, but because she is free, she can raise herself to the level at which this scenario is written and exercise a kind of power over it - the power we call counterfactual.

	The temporality of projects is one of the forms of human experience of time.  This experience is that of the subject who executes a plan he has devised for himself, of which he is both author and actor.  This doubling or "bootstrapping" clearly reveals the demiurgic character of projected time.  Significantly, the French language uses reflexive expressions such as "se décider" and "se déterminer" with the verb "agir" to express the moment of choice when the subject creates a new determinism of which she herself is the object.  Projected time is clearly more "paradoxical" than the temporality of history.  In it we find two features which we have learned to associate with irrational behavior: the subject giving himself a form of power over the past, and the subject looking at himself from outside, as if he were separated from himself.  I hope I have succeeded in showing that these two features are not sufficient conditions for irrationality.

3.	One Paradox of Backwards Induction: the Problem of the Credibility of Promises

	3.1.	Rational choice theory and game theory, two of the principal actors in the rationalist paradigm, are now undergoing a foundational crisis.  This is openly acknowledged by some of their most eminent representatives (for example, Aumann, 1988).  The class of paradoxes we will discuss constitutes one of the most serious symptoms of this.  These are known as paradoxes of backwards induction.  For any decision problem with a finite horizon, whether it involves an isolated actor or a strategic dimension, backwards induction consists in first solving the last step of the problem, the one which, by hypothesis, has no future implications.  Then, sticking to the solution thus determined, a decision is made on the next-to-last step, which at this point in the reasoning has no undetermined future.  Working backwards in time, step by step, the complete solution is in principle reached.  Since the invention of dynamic programming, this method has become the rational way for dealing with this sort of problem.  More than one subject in economics and game theory owes its existence to this method.  Yet in the last few years its very foundations have come to appear less solid than once thought.  My claim is that there is no other foundation for the pretended obviousness of backwards induction than Allais's principle.  I will show that the general framework I have built to contest the universality of this principle is sufficient to resolve the difficulties posed by the method in question.  More precisely, I will establish that the paradox of backwards induction is a Newcomb problem.

	This last result, aside from its intrinsic interest, has important consequences for the meaning we should give to the type of intellectual exercise in which we are engaging here.  We might have thought that the common cause Newcomb problems which we have analyzed were fantasies of philosophers or theologians.  This they are, no doubt, even though (let us consider the Calvinist choice) these imaginary constructions have shaped the world in which we live.  The various forms that the paradox of backwards induction takes are quite another story: the possibility of reciprocal exchange; the stability of agreements, promises and contracts; the effectiveness of threats and deterrence are only a few examples, and it must be admitted there would be no viable human society if people had not succeeded in ensuring the stability of these raw materials of social relations.  That this paradox turns out to be equivalent to problems with a theological aspect or source is thus in itself heavy with meaning.

	Here I will limit myself to two cases: the credibility of promises and the effectiveness of deterrence.  Most authors consider the latter to be the inverse symmetrical image of the former.  The solution I propose reveals that the problem of deterrence is appreciably more complex than that of promising.  I will therefore begin with the latter.

	3.2.	The credo of those who champion free trade is that the economy is not a "zero-sum game."  Exchanges can benefit everyone and, if such is the case, nothing put in their path can last (except that undesirable, the State, with its finicky regulations and policies of redistribution).  All we need to do is to give free rein to the famous "invisible hand," and all will be for the best in the best of all possible worlds.  In theory however there is one condition, rarely made explicit, necessary for things to work out this way.  The two actions which make up the reciprocal exchange which is supposed to benefit the two parties must be simultaneous.  In principle, the least time-lag is fatal.  Let us consider the following situation between Peter and Mary:

Times: 1 and 2;
C: Cooperation; D: Defection.

	A mutually advantageous exchange between Peter and Mary is in principle possible.  It would lead them from their present situations - or the vector (0,0), of which the first component represents the "utility," or any other indicator supposed to order  the preferences, of Peter, and the second that of Mary - to a state (+1,+1) which both prefer.  The problem springs from the fact that for some reason the exchange will only take place if Peter takes the first step (C), in which case he runs the risk that Mary will not take the second step, thus pocketing what Peter gives her without giving anything in return (Mary would thus do D at time 2, ending up with +2 and leaving Peter with -1).

	Backwards induction quickly convinces us that the exchange cannot take place even though it would benefit both parties.  Let us begin with the last step, in other words at time 2, in which it is Mary's turn to act.  It is rational for her - according to the orthodoxy at least - not to reciprocate because she obtains +2 by defecting, against +1 by cooperating.  Note that this reasoning - that of Mary as well as that of the orthodox theorist - is independent of the way that she came to have her turn to act at time 2.  "Only the future matters."  Again the obviousness of Allais's principle rules.

	What should Peter do at time 1?  Thanks to cognitive science, we know that Peter's mind is able to simulate, or reproduce the reasoning that the orthodox theorist lends to Mary at 2.  Note in passing that this implies that Peter believes Mary is rational, or more precisely that she is rational in the orthodox way.  Peter thus has the choice between taking the first step in which case he anticipates that Mary will not take the second and that he will end up with -1; and not moving, in other words doing D, in which case he will obtain 0.  Therefore he does not move and the exchange does not take place.

	Perhaps this disastrous result could be avoided thanks to the institution of promising.  Before the game begins, because it is just as much in her interest as it is in Peter's, Mary promises her partner that she will cooperate at 2 if he cooperates at 1.  A waste of time, according to the orthodoxy!  Mary knows very well that when the time comes, at 2, it will be in her interest to break her promise.  Peter, reading her mind, knows this too.  Even if she swears by all the gods, Mary is not credible.  Therefore Peter does not act.

	Could Peter not trust Mary?  Trust: this is certainly a notion smelling of religion which economic rationality should hold in suspicion.  Yet, in these times of "crisis," this is the word on the tongue of every economist, those who determine policies and, even more remarkably, theorists alike.  It is as if the play of egoistic interests were no longer sufficient to power the economic machine.  It now requires a good dose of this virtue or elixir: trust.  I suspect that this need or lack has to do with the admittedly schematized problem we are discussing.  To this it could be objected that if ever there was a society immunized against the risks of non-simultaneous exchange, it is that which rests on market exchange in which all transactions have the form of transfers of commodities against cash money payments.  We no longer have primitive economies, in which the reciprocity of exchange is dissimulated behind complicated rituals of gift and counter-gift.  (The mechanisms through which reciprocity then truly does take place have provided the occasion for one of the best-fed debates in French-style human sciences: do they involve the hau or "spirit of the forest," according to the Maoris'interpretation which Marcel Mauss merely takes up?  The "synthetic a priori" character of the "rule of reciprocity," according to Lévi-Strauss?  The subtle and hypocritical game of the "practice," according to Bourdieu?)  Furthermore, continues the objection, we live in a civilized society under the rule of law: here exchanges are nothing like the practices often described in novels and movies: exchanging spies on a fog-covered bridge, trading a ransom for a kidnapping victim, all forms of exchange which make visible the absolute necessity that the two movements which make up the exchange take place perfectly simultaneously.  But is that true?  When we pay for commodities with money, what do we give in trade if not a simple acknowledgement of debt, an "IOU" issued by an invisible entity and guaranteed by an empty treasury?  As Marx was well aware, market exchange is nothing but deferred reciprocity, and always more deferred.  The trust deficit which agents suffer with respect to others crystallizes into generalized distrust of money.  We are indeed at the heart of our problem.

	In summary, the market economy vitally needs trust.  The principle of rationality (that of the theorists or the orthodoxy) demonstrates its irrationality and thus its impossibility.  Should we content ourselves with merely contemplating this abyss separating economic practice and economic rationality?  Luckily we can see a way out.  Today this rationality is no longer so self-assured: it has been shaken in its very foundations.  It could be that another conception of rationality can bring the real and the rational closer together.  It might even be able to reconcile them.  It is time to go back to the paradox of backwards induction.

	After all, what is so paradoxical about the orthodox analysis of the Peter and Mary example?  The fact that interacting rational actors mutually condemn themselves to a situation which is disastrous for both?  Rational choice theory is full of this type of situation, beginning with the famous prisoner's dilemma.  If the opposite impression prevails it is due largely to the considerable influence on economic thought of the Walrassian model of general equilibrium, seen as the formalization of the idea of the "invisible hand," or, as Elie Halévy said, of the "natural harmony of interests."

	No, the fact that a growing number of authors are tempted to see a paradox in the very principle of backwards induction is because it seems to suffer from an insidious illness: self-refutation.  This reasoning appears to repudiate itself in its conclusion.  How so?  Let us consider the intermediate result we believed we established: if it is Mary's turn at 2, she will defect.  This is the result on which we built the following, conclusive step which permits us to assert that Peter himself would defect at 1.  But this means that Mary will never get her turn at 2!  Our reasoning has kicked away the ladder which allowed it to climb up to its conclusion and now it is suspended perilously in the air with nothing left to support it.

	If this can be considered an argument, it provokes two opposite kinds of reaction.  The orthodoxy rejects it with a simple shrug of the shoulders.  Others, and I am among them, have the impression they are facing a serious difficulty but that it must be completely reformulated.  Contrary to most of those who share this intuition, however, I do not think that this obstacle can be avoided through technical means.  What is at stake is much more fundamental and concerns our relation to time.

	There are good reasons to reject the argument that this is a case of self-refutation.  If this argument were taken seriously, it would strike right to the heart of decision theory, with perhaps fatal results.  As Shafir and Tversky noted (1993) in a text on "thinking through uncertainty," when one reasons through a decision tree, one is lead to "assume momentarily as true something that may in fact be false" once the overall line of reasoning reaches an end.  In the example discussed, this is exactly what happens in the case of the hypothesis that Mary gets her turn at 2.  As cognitive psychologists, these authors observe that people are extremely reluctant to think in this way, unlike Artificial Intelligence devices for which it is child's play.  Tversky and Shafir even suggest this may be one of the crucial points where the essential difference between natural and artificial intelligence comes into play.

	The self-refutation argument is significant, to some of us at least, not only because it resounds with the psychological structure of our faculties of reason: there are ethical reasons.  In Voltaire's tale, when Zadig sees the hermit murder the nephew of their hostess of the previous night, he is aghast.  What, he cries in outrage, could you find no other way to thank our hostess for her generosity than to commit this terrible crime?  To this, the hermit, who is none other than the angel Jesrad, the spokesperson of Leibniz's system, replies that if that young man had lived, he would have killed his aunt a year later and, a year after that, he would have murdered Zadig.  How do you know that? demands Zadig.  It was written.  Peter refuses to trust Mary because he "knows" that she will not keep her promise.  His refusal makes the falsification of his certainty impossible.  Thus, as they say in philosophy of science, his strategy is auto-immunizing.  Like Zadig-Voltaire, we might want to rebel against such arrogance.  According to more than one moral tradition, if Peter hopes for trust to reign between Mary and him, he has no choice but to prove motion by walking, to jump in, to trust Mary by taking the first step.  However, I would not much want to create the impression I am taking Voltaire's side against Leibniz.  In effect, I will soon suggest that trust may, to a certain extent, be vindicated, if not proven, and I will do this using the metaphor of writing, the same metaphor to which the Leibnizian messenger resorts.

	I have two goals.  I want to show that it is possible to make rigorous the argument according to which the orthodox solution self-refutes; and, at the same time, that reciprocal exchange is both rational and possible.  First we must review a few points.

	3.3.	Most authors accept that the Peter and Mary problem can be solved in terms of precommitment: there are a thousand ways for Mary to "tie her hands" in Peter's eyes and with his knowledge so as to convince him that if he takes the first step, it would be impossible, or at least very costly, for Mary to not take the second step.  Literature is full of stories like this, some of which are utterly fantastic.  Thus, Mary could contract a murderer to kill her if she did not keep her promise.  She could also make a bet with a third party that she would remain faithful to her commitment regarding Peter so that losing her bet by reneging on her promise would cost more than whatever she could gain at Peter's expense.  Such solutions carry risks and are, in any case, very costly in themselves.  Most importantly, however, they come up against some apparently well-established ethical principles.  Is it thus only by alienating her freedom to a third party or a mechanism that Mary can become free?  This paradox is, in the eyes of many, untenable.  Perhaps a solution in terms of commitment, rather than precommitment, could be devised?  Could Mary not commit herself towards herself when she commits herself towards Peter - with a pure translucent conscience, without this relation to herself and the reflexive doubling or bootstrapping which it presupposes implying she be in any way opaque to herself, in bad faith, or self-deceiving?

	A very small number of philosophers (in the Anglo-American tradition I am considering here) think this is possible.  Among them are Edward McClennen (1989), with his notion of "resolute choice" and especially David Gauthier (1988), with his notion of the "rationality of plans."  I will concentrate on laying out the latter's argument, as I interpret it.  At least for the type of problem we are now studying, rationality must be evaluated at the level of plans and not directly at that of actions.  Mary's choice is a priori between four plans, each one consisting in an intention formed at time 0, before the game begins, and an action at time 2.  Suppose, as above, that since Mary's intentions are transparent, Peter can "read" her thoughts.  If Mary intends to reciprocate at 2, Peter sees it and concludes that it is in his interest to cooperate at 1.  The four plans are as follows.  Mary:

Plan 1:	Intends to reciprocate; defects;
		Plan 2:	Intends to reciprocate; reciprocates;
		Plan 3:	Intends to defect; defects;
		Plan 4:	Intends to defect; reciprocates.

	From all points of view, Plan 4 is a non-starter.  For Mary, Plan 1 would be the ideal if it were possible, but it is not, Gauthier argues: it is certainly possible to form the intention to x at one time and to not-x a minute later, but one cannot form the meta-intention (the plan) to do that (Gauthier does not develop the justification for this argument which, it might be imagined, would require some refinement).  Two possibilities remain and it is clear that, given Peter's reaction, Plan 2 is better for Mary than Plan 3.  Thus she adopts Plan 2 and this is possible for her because she is convinced it is rational.

	The orthodox reply is that Plan 2 is "dynamically inconsistent."  At time 2, Mary will not reciprocate because doing so would be against her interest.  She knows this at time 0.  It is impossible for her to form the intention to do something which she knows will be, when the time comes to do it, irrational for her to do.  As David K. Lewis (who places himself in the orthodox camp) notes critically, Gauthier can only claim the contrary because his thesis is that rationality must flow "from the rationality of intention to the rationality of action, rather than vice versa" (Lewis, 1984).  For Gauthier (1984), the fact that Mary was able to establish the rationality of Plan 2 gives her a "reason to act" (according to the plan) at time 2 which overrides her preferences at that time.  This is unacceptable to the orthodoxy.  This "holism of plans" is too contrary to the postulates of methodological individualism.

	In this debate internal to American philosophy, the defence of my position requires finesse because it finds itself, as it were, caught in the crossfire.  On one hand I wholly share the conviction of Gauthier and McClennen that one can and should save the possibility, rationality and effectiveness of promises in situations like Peter and Mary's.  On the other hand I hold that there is a high philosophical price to pay for this, a price much higher than that which these authors are ready to pay.  If the orthodoxy accepts my demonstration it will certainly be delighted, but for the wrong reason: it is equivalent, according to them, to the proof that reciprocal exchange is impossible.  More precisely, Gauthier's method remains a form of consequentialism, a consequentialism of plans if one wishes, in opposition to that of actions.  Now, according to me, if one hopes to save the rationality and possibility of reciprocal exchange, one absolutely must renounce consequentialism and put oneself in "projected time."  This is what I will now attempt to show.

	3.4.	In the first stage I will present a demonstration which is very unsatisfactory from at least three points of view: 1) it is purely formal and syntactic; 2) it retains only the metaphorical characterization of the concept of projected time, in other words the image of the Great Scroll on which everything "is already written;" 3) it resorts to the concept of "rational expectation," which carries a heavy metaphysical load and, more importantly as we will discover in the end, suffers from incompleteness because it is fundamentally ambivalent.  In the second stage I will attempt to deconstruct the metaphysical residue and give meaning to what will have been nothing but a formal exercise.

	Let us call "rational expectation path" or, for short, "rational path," any path in a decision tree which satisfies the two following conditions:

		a)	It is temporally consistent.  This means that it corresponds to what could be an actual sequence of events, each one leading to the next.
		b)	It is compatible with the assumption of rational expectation.  The expectations of the agents are compatible with the "true" model of the problem and their behavior is rational given these expectations.

	In the Peter and Mary example, we see that there are three temporally consistent paths:

	If we consider condition b), we see that the second of these paths obviously does not satisfy it. The orthodox and the heterodox cannot but agree on that: at 1 Peter is supposed to know that Mary will defect at 2; it is thus irrational for him to cooperate at 1.  There are thus two candidates to the status of rational path: (Peter,D) and (Peter,C; Mary,C). The rational path is necessarily one of these two possibilities: everyone agrees on that.Which of the two is the rational path, that's where views are at odds. For the heterodox it is the second, to which the orthodox object that it violates condition b); but the heterodox reply that one can say that only on the basis of the Allais principle, the universal validity of which is precisely in question. For the orthodox, the rational path is (Peter, D); the heterodox object that this result rests on the claim that it is true at t=1 that Mary defects at 2 even though Peter chooses at 1 to defect (self-refutation argument). Before delving into this controversy, let us set out formally what we have just discovered.

	Suppose that (Mary defects at 2) - or (Mary,D) for short - is part of a rational path.  From this we deduce:

		(Peter cooperates at 1), due to temporal consistency;
		(Peter defects at 1), due to rational expectation.

	Thus a contradiction.  We conclude that (Mary,D) is part of no rational path.  It follows that the following property is valid for the rational path, whatever it is:

Either (Mary does not get to play at 2) or (Mary reciprocates at 2)

	This proposition is equivalent to:

(6) If Mary plays at 2, then she reciprocates at 2;

	or:

		(7) If Peter cooperates at 1, then Mary cooperates at 2.

	At this point we might be tempted to cry victory.  It seems we have succeeded, using a self-refutation argument, in doing away with the possibility Mary might defect at 2 if she gets a chance to play at that time.  Nothing seems to stand in our way to concluding that Peter, knowing (7), concludes that it is rational for him to cooperate.

	This would be all too easy.  We must not forget that (6) and (7) are only properties of a rational path.  They tell us nothing about what it would be rational for Mary to do at 2 if she should have her turn at that time.  The orthodoxy has no trouble accepting (6) and (7) insofar as they are properties of the rational path.  Their path, or (Peter,D), satisfies them perfectly, in other words trivially, by falsifying the antecedents of these conditional propositions.  In their oecumenism, these propositions provide absolutely no way to decide between the two camps.

	Obviously the orthodox theorists do not stop here.  They have another fundamental concept in their toolbox: the equilibrium of rational expectations.  The concept of equilibrium in game theory is such that it specifies a choice at each node of the decision tree, even at those nodes which will never be reached by a sequence of events constituting a rational path.  The information contained in the equilibrium is thus very rich since it includes, as well as the specification of a path actually followed in time, a whole set of counterfactual propositions.  Thus the set of choices which constitute an equilibrium will generally not satisfy the condition of temporal consistency (but it will obviously respect, by construction, the condition of rational expectation).

	In the case of the example given, the equilibrium of rational expectations is, according to the orthodoxy, (Peter,D; Mary,D), or:

	Backwards induction provides the justification for this particular equilibrium, which is clearly not temporally consistent.  In the name of Allais's principle, the orthodox theorist can assert:

		(8) If Mary got to play at 2, she would defect at 2.

	The orthodox theorist, rightly, feels no contradiction in asserting both (6) and (8).  Again, (6) simply expresses a property satisfied by the rational path, and the rational path for the orthodox theorist is (Peter,D).  (8) is a "subjunctive conditional" which expresses a counterfactual proposition.

	We will now attempt to draw out the implications of the Great Scroll metaphor, which characterizes projected time.  Since everything is "already written," there is no way, not even a counterfactual way, to escape the rational path which appears on the scroll in question.  More precisely, any subjunctive conditional expressing such a counterfactual will immediately be reduced to an indicative conditional describing a property of the rational path.  A question like:

(9)	What would it be rational for Mary to do if she got to play (at 2)?

is translated as follows:

(10)	What does Mary do at 2 on the rational path if she gets to play at 2 (on the rational path)?

	Since proposition (6) is true of the rational path, whatever it is, it provides the answer, which we hurry to translate into the language of counterfactuals: 

(11)	If Mary got to play at 2, then she would cooperate at 2;

	which is equivalent to:

(12)	If Peter cooperated at 1, then Mary would cooperate at 2.

	Peter is rational and anticipates (12): from this he concludes that it is rational for him to cooperate at 1.  Therefore he cooperates, and so does Mary.  Reciprocal exchange is both rational and possible.

	Remember that we do not claim to have shown anything here.  We have given ourselves a syntactic rule (the translation operation) and we have applied it mechanically, without attempting to endow it with meaning.  Now we must interpret what we have done.

	3.5.	We must return to the origin of the bifurcation of the two temporalities (see section 2.2.).  Projected time, we note, corresponds to the option of taking the temporal linkage to be fixed (in other words, valid in all possible worlds), and "sacrificing," in a certain way, the fixity of the past.  Propositions (11) and (12) thus express a necessary relation, valid in all possible worlds.  This can also be written as:

		(13) (Peter cooperates at 1)    (Mary cooperates at 2),

and expressed in the following way: the fact that Peter cooperates at 1 is the "writing" in the past of the future fact ("future contingent "): Mary will cooperate at 2.

	This is the option which allows counterfactual questions regarding the rationality of choices to be reduced to factual questions concerning the rational path.  Once again using the metaphor of the Great Scroll, what is "written above" has the authority of an intangible rule.  One might object that this turns the rule into a sacred object: in other terms this is "superstitious rule-worship" (J.J.C. Smart).  Before justifying this approach by analyzing its conditions of possibility, I would like to remark that the orthodoxy is not safe from a similar objection.  It too must pay a high metaphysical price.  The orthodoxy arrives at the subjunctive conditional (8) in virtue of the principle of the fixity of the past: no matter what past path lead Mary to have her turn at 2, only the (future) consequences of her present choice have any relevance (Allais's principle).  Very well!  Yet is not the domain of validity of that principle stretched beyond reasonable limits when, as in this case, it is applied even to decision situations to which no past path leads?  This too strongly resembles the sacralization of a principle.

	The syntactic exercise in which we engaged above took for granted the concept of rational expectation, which plays such an important role in economic theory today.  The concept is in no way above suspicion, and our little exercise will at least have the merit of revealing that it was not well-formed since it was unable, alone, to separate the two rational paths, the orthodox and the heterodox.  This ambivalence springs from the ambiguity of the notion of "perfect foresight."  In our model, Peter is both a predictor and an actor.  His action is closely linked to his prediction: in a certain way, his action writes his prediction in the material world since if Peter predicts that Mary will cooperate, he cooperates himself, and if he predicts that she will defect, he too defects.  He is supposed to predict Mary's action perfectly.  What does this mean?  This can be understood in two ways, which differ as N2 differs from A2 at the point where the two temporalities branch apart.  Peter could be essentially omniscient, in other words, omniscient in all possible worlds, or he might be so de facto, in other words, only in our world (Plantinga, 1986; Dupuy, 1992).  This is determined by Mary when she reasons at 2.

	In the first case, she reasons as follows.  If I was to cooperate at 2, Peter would have foreseen it at 1 and, being rational, would have cooperated himself.  If I was to defect, we would be in another possible world (since I am free), in which Peter would also be omniscient.  He would thus have foreseen that I would defect and he would have defected too.  But in that case I would not have been able to have my turn at 2, contrary to my premise: I must thus set aside this possibility.  This is where the self-refutation argument appears.  If it is here validated, it is because Mary's hypothesis of the essential omniscience of Peter automatically leads her, as we have seen, to give herself, as she reasons, a counterfactual power over the past.  Mary logically concludes that, if she were to have her turn at 2, she would cooperate.  This reasoning is strictly equivalent to that which we performed in section 3.4.  It also shows that the Peter and Mary problem is equivalent to the Newcomb paradox in its original form, which brings in an omniscient predictor who is capable of acting on the state of the world according to his prediction (Dupuy, 1992).

	If Mary attributes Peter with the power to predict perfectly, but only in our world, her reasoning develops quite differently.  Peter foresaw what I was going to do and he recorded this mental act in the material world by acting in consequence of it.  What I, Mary, will in fact do at 2 will in no way alter this past occurrence.  I thus take the past to be fixed when I act.

	Mary cannot seriously attribute Peter with an omniscient power, essential or de facto.  Fantastic hypotheses like this are found only in economics textbooks.  We must get rid of this metaphysical residue.  Peter has no privileged access to the future, but he has certain access to Mary's mental state at the time preceding the moment at which he must act.  He can "read" Mary to see if she has the intention or not to cooperate at 2.  This is certainly far from providing him with a sufficient guarantee.  It could be that at 0, Mary had the intention to cooperate at 2 but when the time comes she does not act in conformity with this intention.  It could even be that Mary only "has" this intention, or manifests it, strategically, in order to bluff Peter.  Peter thus needs much more than this.  He must convince himself that Mary's intention at 0 to cooperate at 2 is the writing in the past of the future contingent: Mary will cooperate at 2.  Mary's task is to convince him of this.  It must be granted that she will only succeed insofar as she can convince herself.  The question therefore becomes: can she do it?  Alas, the answer is negative, as the following argument shows.

	3.6.	Gregory Kavka (1983) challenged the philosophical community with a particularly cunning puzzle.  Kavka, a specialist of the moral and political philosophy of Hobbes, is known for the positions he has taken in the American debate over nuclear deterrence.  He has come out against the very principle of nuclear deterrence, and we will refer to his analyses in the part of this work devoted to threats.  His puzzle is known as the "toxin puzzle."  A billionaire, who has made his fortune in cognitive science, comes to you and proposes the following exchange.  "You see this vial," he says, "it contains a toxin which, if you swallow it, will make you as sick as a dog for two days but will not kill you and will leave no after-effects.  If you swallow the contents of this vial, I will pay you a million dollars."  You are already rejoicing over this unexpected deal because you consider that the physical discomfort will be greatly dwarfed by the fortune you have been offered, when your eccentric acquaintance adds: "I am not even interested in whether or not you actually drink the toxin.  I will be satisfied if you form the intention to do so.  I have brought along this machine I have invented which is able to detect intentions precisely.  You will attach it to your brain tonight at midnight and it will then record whether or not you have the intention to drink the toxin tomorrow at noon.  And, since I am generous, I won't even wait for you to drink it to give you your reward.  If the machine detects a positive intention, you will find the million dollars in your bank account first thing tomorrow morning."  On this, the billionaire leaves you to your bitter thoughts because, as a well-informed philosopher of mind, you have quickly understood that the pot of gold which appeared to be at your fingertips, or rather your lips, has slipped away forever.

	Let us reason like the orthodoxy.  Tomorrow at noon, whether or not you have found the million dollars in your account, you have no reason to drink the toxin, and you have a very good reason not to drink it.  The past is what it is, and your decision will not change it (Allais's principle).  There is a dominant strategy, not to drink the toxin, and it is the rational strategy.  You know this from now on, and thus also tonight at midnight.  Since you cannot will yourself to form an intention, it is impossible for you to form the intention to do X if you know that when the time comes it will be unreasonable for you to do X.  It is thus impossible, tonight at midnight, to form the intention to drink the toxin tomorrow at noon.  The true poison is not that in the vial, as you thought, but indeed the billionaire's generosity.

	It is easy to see the isomorphism of the toxin puzzle and the promise problem.  Whatever the dominant views in cognitive science, which include belief in the reality of mental states such as beliefs, desires and intentions, the machine for detecting these states is, and it seems will remain, fictional.  In contrast, the "machines" for attributing mental states to various cognitive systems, be they human, living, artificial or collective, have been around a long time and are in abundant supply: they are human minds.  The translation of the promise problem into the terms of the toxin puzzle is crystal clear.  The toxin is Mary's renunciation of the profits of her dominant strategy, defection.  The million dollars is the gift Peter gives her by letting her have her turn, and the link between the intention to drink the toxin and what appears to be the reward has its equivalent in Peter's rational decision.  The conclusion is the same in both cases.  At 0, Mary cannot form the intention to cooperate at 2 because she knows that when the time comes it will be irrational for her to do so.  Thus she will not have her reward.

	That was the orthodox argument.  Can it be refuted using the projected time approach?  Alas, we must give up this hope because of the nature of intentions.  Remember that in order for us to be in projected time, the portent - the event we label C - must appear as the writing in the past of the future contingent which it announces.  In other words, the temporal link between these two events must be considered as valid in all possible worlds.  However, the link between the intention at 0 to do x at t, and the action of doing x at t, cannot be held to be fixed in this sense.  The analysis of the toxin puzzle explains this.  The subject is free to do Not-x rather than x, but this in no way endows her with a counterfactual power over the past (here, the past intention) which defines projected time.  Suppose, in effect, that the subject determines that one of the options is rational and that this option is, say, x.  It would not be reasonable for her to do Not-x at t, therefore she cannot form the intention to do it at 0.  Consequently, the fact that she is free to do Not-x gives her no power to form the intention to do Not-x at 0.

	3.7.	Should this failure be the end of the line for our inquiry?  I think not.  The analysis of what differentiates the promise problem from the toxin puzzle will allow us to move on.  In the latter, the subject is connected to a machine; in the former she is interacting with a person.  The link between the intention and the reward is, on the one hand, an automatic process imposed by the capriciousness of a being whose interest in the affair is inscrutable; on the other hand, the link can be an agreement, contract or convention in the form of a fixed rule (always in the sense of: valid in all possible worlds) between the actions of the parties concerned.  I repeat that my ambition is not to prove this possibility (this would, it seems clear, be bound to fail).  In the framework set up here, and more particularly concerning the issue of the scope of Allais's principle which we have been studying since the beginning, I simply want to bring out the formal conditions of this possibility.

	Ethical issues have no bearing, in principle, on the toxin puzzle.  This makes it even more significant that certain subjects (again selected from Californian, in other words Puritan, social groups) claim to be able to hit the jackpot because they spontaneously introduce a parasitical notion which did not figure among the givens of the problem: merit.  There is a way out for he who considers that, in spite of the billionaire's apparent, deceptive laxity on this point, he has the right to the million only if he pays what seems to him to be the price: the discomfort caused by ingesting the toxin.  A world in which he does not drink the toxin at noon is a world in which there is no possibility he will have received the million.  We can try as hard as we want to show him that he will have already received or not the million when it will be the time for him to decide to drink or not, but he sticks to his guns.  He is not affected by the argument according to which he inverses the order of time.  This determination is what saves him.  In effect, he now has a good and decisive reason to drink the toxin: if he does not do it, he forbids himself to have the million.  This is his reasoning when his intentions are detected, thus before he knows if he has passed the test.  Since now he has a good reason to drink, he is able to form the intention to do so - and thus pocket the million.  Contrary to what Gauthier asserts concerning his own solution, here there is no inversion of the usual relation between the rationality of the action and that of the intention - the rationality of the intention determining, according to Gauthier, that of the action.  Rather, there is simultaneous, reciprocal determination of the rationality of the action and the rationality (and thus the possibility) of the intention through a bootstrapping operation which frees the heterodox solution from the orthodox trap.

	We want to show that at time 0, Mary can reasonably make a promise to Peter and, through him, to herself to cooperate at 2; and, if Peter makes the first move, to make the second, thus fulfilling her promise.  The action which constitutes this promise is the inscription in the past of the future contingent: I will cooperate at 2.  The temporal link between these two actions is fixed, or valid in all possible worlds.  A world in which Mary defects at 2 is a world in which it is excluded that she promised at 0 to cooperate.  At 0, Mary thinks thus: if I were to defect at 2, then I would not have promised at 0 to cooperate.  But then Peter would not have given me my turn and I would not be in a position to make any decision at 2.  Therefore Mary now has a good and decisive reason at 0 to cooperate at 2: if she does not do it, she forbids herself the benefits of the exchange by not giving Peter any reason to make the first move.  With this decisive reason to cooperate, she can make the intention at 0 and express it to Peter in the form of a sufficiently firm promise to incite him to embark on the adventure of trust.  The self-refutation argument is thus perfectly legitimate here.  We are obviously in what I call projected time.  Two of its features are clearly visible.  Mary takes distance from herself, inferring the state of the world through the observation of her actions.  She gives herself, within her reasoning, a counterfactual power over the past.

	Let us call this a "Kantian" promise.  In effect, its bootstrapping form evokes the Kantian (and Rousseauian) concept of autonomy: the ability to limit one's individuality by giving oneself a transcendent, fixed law or rule, and following it.  This self-limitation, we should note, is radically different from a solution consisting in "tying one's hands."  The former (commitment) is an act of free will: it in no way suppresses liberty.  Rather, it is the highest manifestation of freedom.  Having made the Kantian promise to cooperate, Mary nonetheless remains perfectly "free" (in the sense of free will) to defect.  This is why this promise requires projected time in order to be effective.  The fact that one has tied one's hands (precommitment), in contrast, implies that one limit, in the temporality of history, one's freedom of choice.  The Kantian promise is undoubtably one of the summits of ethics.  Yet we detect at its very heart the two features we have learned to associate with the irrational: the subject attributing himself with a power over the past and observing himself from the exterior like another self.  It seems to me appropriate, in conclusion, to paraphrase the last phrase of Donald Davidson's classic article on irrationality (1982): "A theory that could not explain irrationality would be one that also could not explain our salutary efforts, and occasional successes, at self-binding and self-transcendence." (The original ends with the words: "self-criticism and self-improvement.")

4.	A Second Paradox of Backwards Induction: The Problem of the Effectiveness of Deterrence.

	4.1.	Deterrence and promising are equally important for the organization, and the very existence, of human societies.  Yet, as I have already mentioned, the problem of the effectiveness of deterrence is of a markedly higher level of difficulty than that of the credibility of promises.  The reason for this difference is in itself of utmost interest.

	Consider the following case.  Alter Ego contemplates attacking Ego.  If it attacks, Ego has the choice of yielding - in which case it loses, for example, part of its territory, market or assets - or of counter-attacking, which could lead both adversaries to mutual disaster.  In game form, this situation can be represented as follows:

	Reasoning by backwards induction, the results are: If Alter Ego has attacked, then Ego gets to play at 2 and it is in its interest to yield.  Alter Ego thus obtains +1, as opposed to 0 if it renounces.  Thus, it attacks, and Ego provides no resistance.  This is the first equilibrium, but in theory there is a second, supported by Ego's threat, deterrent in principle: "If you attack me I will retaliate."  Alter Ego renounces in this case.  Ever since the German game theorist Richard Selten's seminal paper (1975), this second equilibrium has generally been considered unacceptable - even though Ego's deterrent strategy costs it nothing since Alter Ego renounces.  In effect, suppose that Ego were in a situation to make good on its threat: if it is rational, it will avoid doing so since it will be too costly for it.  Its threat is not credible.  The corresponding equilibrium is "imperfect" and deterrence is revealed to be fundamentally ineffective. The only subgame perfect equilibrium is that determined through backwards induction.

	The concept of imperfect equilibrium could not have been discovered in the promise case because it has only one equilibrium, that of backwards induction.  This point, which appears to be purely technical, merits our attention for it reveals a profound difference between threats and promises.  The reciprocal exchange between Peter and Mary is not (even) an equilibrium because if Peter cooperates, it is in Mary's interest to defect.  To the contrary, deterrence is an equilibrium, even if it is rejected in the end since it is imperfect.  Presenting these two problems in this way could be misleading because it seems to imply that saving the rationality of deterrence (which is "at least" an equilibrium) is easier to do than saving the rationality of reciprocal exchange (which is "not even" an equilibrium).  However, as we shall see, the opposite is true.  In fact, the purely formal characteristic of equilibrium adds nothing, especially when, as is the case here, it does not even clothe itself in the finery of self-evidence like backwards induction.  Let us go back to what makes deterrence an equilibrium.  To do this we will play the favorite game of game theorists, which is to proceed using as few words as possible in order to ensure formal rigour.  (Ego,R) and (Alter Ego,r) are in equilibrium, we are told, because:
		a) (Alter Ego,r) is Alter Ego's best response to (Ego,R).
We can accept this, even though we see here the insistent problem linked to the temporal inconsistency of the equilibrium: how can Alter Ego know that Ego will do R since it is not given a chance to play?  The same question asked about the single equilibrium in the promise case at least has an answer based on a principle considered to be indisputable: Allais's.  But here if Ego does R, it will violate this principle and can only be justified by the second term of the argument:
		b) (Ego,R) is Ego's best response to (Alter Ego,r).
Here we are truly bordering on insanity.  The problem is not that (Ego,Y) would provide Ego with the same payoff since, by convention, we attribute to (Alter Ego,r; Ego,R) and to (Alter Ego,r; Ego,Y) the same payoff, i.e. the one that corresponds to their common temporal path: (Alter Ego,r).  The problem is that speaking of Ego's "response" to (Alter Ego,r) is radically meaningless.  Let us revert to words in order to express this.  That Ego "retaliates" or "yields" to Alter Ego implies that Alter Ego has attacked, and this implication does not hold in virtue of any hypothesis about rationality: it holds analytically.

	Game theorists were well inspired to deprive the imperfect equilibrium of the right to inhabit the City of Rationality.  If they had kept it in sight, they would have been forced to question the concept of equilibrium itself.  Most game theorists, following the example of many economists, do not take a line of thought or argument seriously unless it can be put in purely syntactic form.  It is no coincidence game theory is of the same generation as cognitive science: thinking is reckoning, in other words blindly following an algorithm.  Clinging to the postulate, which is now abandoned by logicians themselves, that syntax is separable from semantics, they push purity to the point of satisfying themselves with syntaxes to which no semantics can be ascribed.

	Coming back to the deterrence game, an even more depressing classical result of the theory is that our above conclusion about the ineffectiveness of deterrence, remains unchanged if the game is repeated any finite number of times.  Suppose that Ego has n rivals which, one after the other, plan to attack it. In the last round, the static game argument is fully valid since there is no future: the last rival attacks and Ego yields.  In the before-last round, since the last round has already been determined, everything occurs as if this were the last round, and the same thing happens.  So it goes , from round to round, from which it again appears that the only perfect equilibrium is that in which the n rivals attack without ever encountering retaliation from Ego.

	This result is not only depressing, it is paradoxical.  It contradicts the following intuitive reasoning, which expresses what we ordinarily mean by deterrence, and of which experience generally succeeds in showing the pertinence: even if it is costly in the beginning for Ego to respond aggressively to the first rivals who attack it, it will come out ahead in the long run because observation of its past behavior will convince later rivals that it would be better to refrain.  Knowing this, the first rivals themselves could be lead to renounce attacking, thus Ego would never have to execute its threat.  The appearance or reputation of a "tough guy" which it would acquire in this way, through its behavior or its potential behavior, would make the deterrence strategy effective.  This argument, however, borders on paradox. What is the foundation for Ego's reputation if its behavior is the only source of its reputation and if, in fact, because deterrence is effective, Ego never has to act?  The construction of reputation presents itself as a process at risk of self-refutation.

	Four games theorists from Stanford (Kreps, Wilson, Milgrom and Roberts) have succeeded in showing that it is possible to return to the intuitive argument and uphold its result, namely the effectiveness of deterrence, if one makes a very tiny alteration to a hypothesis which has remained implicit in the backwards induction argument.  This hypothesis is that the givens of the problem, in particular the fact that the players are rational, are Common Knowledge (CK): each player knows them, each one knows that the others know them, etc., to infinity (Kreps et al., 1982; Kreps and Wilson, 1982).  Suppose that the rivals are not sure that it is rational for Ego to yield if it is attacked, or that Ego is rational.  They assign a small probability to the opposite case.  In this world of imperfect, asymmetrical information, we define a concept of equilibrium which generalizes the idea of perfect equilibrium: sequential equilibrium.  We can then construct models in which the sequential equilibrium is the same as the intuitive solution.  Everything occurs as if the rivals decided their actions according to the representation they form about Ego, its reputation, using observations about its past behavior.

	Escaping the deterrence paradox using the notion of reputation is not without its own formidable problems.  However, I will not discuss them here because I want to defend the following thesis: deterrence can be effective and rational even in the first case, the one in which there is only one rival, Alter Ego.  Before doing this, as we leave the slightly cramped universe of game theory, I must sketch out the debate which has animated American analytical philosophy regarding deterrence paradoxes (and in particular nuclear deterrence).

	4.2.	Over and above their sometimes violent disagreements, those who participate in this debate have two features in common which absolutely set them apart from game theorists.  First, they consider that the way game theory conceives of deterrence simply misses the key aspect of what falls under this term.  Deterrence is not an "equilibrium," perfect or imperfect.  This is not an issue: it is an act, more importantly a speech act.  It is a speech act which expresses an intention, more specifically the conditional intention to retaliate if one is attacked.  Coming back to our first model, we would thus suppose, as we did in the promise case and the toxin puzzle, that it is at time 0 that Ego, if it can and decides to do so, forms and expresses its intention (here to counter-attack at 2 if it is attacked at 1).  The second point the authors we will be speaking of share is that they take the ethical dimension of the deterrence problem to be inseparable from the issue of its rationality.  Gregory Kavka, the inventor of the toxin puzzle, has even suggested (1978) that, when the stakes N are high (nuclear danger), the point of view of instrumental rationality (rationally employ all means to avoid the hecatomb) becomes the ethical point of view.  On this double foundation, three sharply delineated types of positions have appeared.

	The orthodoxy, faithful to backwards induction no matter what, concludes that since it is wrong (in other words both irrational and unjust) for Ego to retaliate at 2, it is just as wrong, and indeed impossible, for it to form, at 0, the intention to do such a thing.  They thus take sides with the game theorists who assert that deterrence is fundamentally irrational and ineffective.

	Gregory Kavka (1978) (followed to a certain extent by David K. Lewis (1984)) has defended a more complicated view, though he too concludes that deterrence is profoundly wrong.  According to him, it is both just (in other words rational and morally acceptable) to form and manifest at 0 the intention to counter-attack - because that can have a deterrent effect - and wrong or unjust to execute the threat if one is put in the situation to do so (in other words if deterrence has failed).  This is a first paradox because it thus compromises a moral principle which we have considered, until the age of nuclear deterrence, to be an axiom: "to intend to do what one knows to be wrong is itself wrong" (Kavka, 1978).  Kavka, however, does not stop there (unlike Lewis, for which the latter is accused of incoherence by Gauthier (1984)).  Kavka, like the orthodox theorists, believes in Allais's principle, and thus in backwards induction.  He must thus conclude that if Ego is a "rational and morally good" person, it will be incapable of forming the intention to retaliate (this is where the toxin puzzle comes in), even though it holds the formation and manifestation of this intention to be a rational, morally justified action.  Only by deliberately accepting to "corrupt itself," by alienating its freedom to a third party or a mechanism (the precommitment solution: note the automatic retaliation devices searched for by the Strategic Defence Initiative of the Reagan years) can it perform an act (threaten the adversary with retaliation) which it knows to be just - and this self-corruption itself appears just.  These last two features also run up against moral principles we hold to be true or even analytic.  The general conclusion is equivalent to an unequivocal condemnation of (at least nuclear) deterrence, which is pronounced guilty of destroying the very foundations of our moral judgment.

	David Gauthier (1984), true to his view that the evaluation of the rationality of intentions and plans comes first, and then determines that of the rationality of actions, has defended the position that it can be rational (and just), and therefore possible, for Ego to form the intention to retaliate.  Thus, as a result, if deterrence fails it would be rational and just to execute the threat.  More recently, Gauthier seems to have retreated from this position and recognized that cases of threats do not fall under the jurisdiction of the same general principles as those of promises.

	I would now like to argue in favor of Gauthier's initial thesis, that deterrence can be effective and rational, while using, as I did in the promise case, a conceptual framework different from his.  However I would also like to confirm his present suspicions: the philosophical price to pay for supporting this thesis is very high, much higher than it was in the case of the promise (and undoubtably much higher than Gauthier is willing to pay).

	4.3.	As earlier, I will alternate blindly syntactical arguments and attempts at interpretation.  The first idea which comes to mind is obviously to apply to the deterrence case the process which had such good results in the promise case - in the hope that we will be able to show that deterrence is effective in projected time.  Wrong!  Suppose it is written on a rational path that Ego retaliates at 2.  From this we deduce that at 1 Alter Ego both attacks (temporal consistency) and renounces (rational expectation).  From this contradiction we infer that on all rational paths we have: "If Ego plays at 2, then it yields at 2."  The translation rule between indicative conditionals and subjunctive conditionals which characterizes projected time then gives us: "If Ego got to play at 2, it would yield at 2."  This proposition is the same as the one to which we are lead using backwards induction.  The rational path is the same in both temporalities.  Whether in projected time or in occurring time, deterrence reveals itself to be hopelessly ineffective.

	This observation can be verified by defining Alter Ego's role as an omniscient predictor of Ego's behavior.  What distinguishes projected time is that in it this omniscience is essential, or true in all possible worlds.  The question "Can Ego retaliate at 2?" is thus equivalent to another question: "Can Alter Ego predict that Ego will retaliate at 2?"  Obviously the response to the latter is negative, for if Alter Ego predicted retaliation, given that it is not only a perfect predictor but also a rational agent, it would refrain from attacking so that its prophecy could never come true.  Thus Ego can no more retaliate at 2 in projected time than in occurring time.  It is easy to see what happens here.  In the case of deterrence, projected time's logical evil of self-refutation affects not the solution we wanted to eliminate (as it did in the promise case), but the solution we hoped to save: the effectiveness of deterrence.  This is the bad news.

	In the promise case, it was not enough to show that reciprocal exchange was possible and rational in projected time: we also had to prove that one could place oneself in its framework.  This was no easy task since the simple play of intentions proved to be ineffective.  We had to bring in the concept of "Kantian promise," or a promise fulfilled in all possible worlds.  There is no point in hoping to slip deterrence through an escape hatch like this.  A fixed commitment (in other words valid in all possible worlds) which Ego would make at 0 to retaliate at 2, if possible, could only lead to the projected time solution, and we already know that it is identical to the orthodox solution.  Nonetheless it is interesting to take this angle of approach in order to appreciate the nature of the problem.

	Suppose that the commitment Ego makes at 0, in the form of a threat, can be held to be fixed.  This commitment is then the writing in the past of the future contingent  which expresses its behavior at 2.  Now, how shall we formulate this behavior?  Certainly not as "Ego will retaliate at 2."  Ego's commitment, in effect, is not and cannot be categorical; it is necessarily hypothetical or conditional: "Ego will retaliate at 2 if it is attacked at 1."  This point, which was not emphasized in the promise case because it was less relevant, is crucial in the case of deterrence.  If, in fact, Ego can make such a commitment, Alter Ego will find it rational to renounce and Ego will not get to play at 2.  Thus, even if Ego's commitment is fixed, the temporal link between the events "Ego commits itself at 0 to retaliate at 2" and "Ego retaliates at 2" is so little fixed that it is violated in all possible worlds in which Alter Ego reacts rationally by renouncing.  Ego's commitment cannot therefore be considered the writing in the past of its actual counter-attack.  This commitment announces nothing on the rational path.  This is, in the final analysis, the source of the self-refutation of deterrence in projected time.  Here we meet up with the paradox of deterrent intention, which Gregory Kavka brought to our attention.  The contents of this intention, what it is that it tends towards, is an action which the agent has no...intention (desire) whatsoever to accomplish.  This is the fundamental difference between promising and threatening.  A sign does not lie, as Gauthier notes (in Frankel Paul et al., 1988): if the second player gets to play at 2, in the promise case it is because her plan has succeeded; in the deterrence case it is because it has failed.

	All of the above suggests that, in projected time, deterrence is a self-refuting ideal insofar as it is perfect.  When it is perfect it prevents Ego from having its back to the wall.  Neither Alter Ego nor Ego itself can know in projected time what an action promised to nothingness means.  We must not forget that in this temporality, the only source of information for counterfactuals is the rational path.  If the latter corresponded to successful deterrence - or (Alter Ego,r) - there would be no answer to the question: "What would Ego do at 2?" - in other words "What would Ego do if it found itself faced with its responsibilities because its attempt at deterrence had failed?"  The success of deterrence presupposes, to the contrary, that it is known (by both Ego and Alter Ego) that Ego will retaliate if attacked.  This is the source of the self-refutation which weighs on deterrence.  The impossibility of giving a meaning to what might happen, counterfactually, off the rational path might be pronounced a major failing, because it is constitutive, of projected time.  (It is perhaps easier to see now why I chose the name "projected time."  It is an implicit reference to an aspect of Sartre's philosophy and also to that of Bergson.  These philosophers were certainly very distant from the conceptual framework we are using here, but for them the possible was nothing but what is in effect presented by a free action or choice.  For a very enlightening clarification of this difficult issue, see B. Sève, 1993.)  There are two answers to this.  First, projected time is our only hope to salvage the effectiveness of deterrence given there is no way to appeal the judgment of occurring time - and if we set aside solutions consisting in "tying one's hands" (precommitment), which alienate freedom in order to save it, as Kavka has pointed out.  Second, in spite of its extreme abstraction, the claimed failure of projected time strongly echoes a universal existential experience here.  Phenomenologically: in order to preserve my integrity, I menace others with retaliation if they attack me.  Suppose this expression of my will is successful: this success is also necessarily a failure because it leaves unanswered the question which I and the others ask ourselves: what would I have really done if I were placed before the fait accompli?  Facing this question, our finitude as beings immersed in time remains hopelessly silent, which can be a source of deep anxiety.  Sartre's philosophy and theatre have powerfully staged situations of this type.

	4.4.	There is however a way to break the circle of self-refutation.  As we have said, the temporal link between the events "Ego commits itself at 0 to retaliate at 2" and "Ego retaliates at 2" cannot be held to be fixed even if the commitment is held to be, because in all possible worlds in which Alter Ego acts rationally, it is not true that Ego retaliates at 2.  Nonetheless there are possible worlds in which Alter Ego decides, against all reason, to attack.  Then, since Ego's commitment is fixed, it is true in these worlds that it indeed retaliates at 2.  Let us include these cases in the reasoning.  Of course, we are now changing the hypotheses since we are allowing for errors.  There are possibilities other than the alternative: deterrence is effective or it is not.  For example, deterrence is almost certainly effective, but there is a chance it might not be.  Could it be that imperfect deterrence escapes the self-refutation which condemns perfect deterrence?  The answer is positive, and we have an intuition why this is so.  "Everything is already written," is granted since we are in projected time, but there are errors in the script.  It might be that the rational path includes "Ego retaliates at 2" without leaving us defenceless against the objection that Ego would not get to play at 2, because there might now be a possible path, due to an error in transcription, which indeed gives Ego a chance to play at 2.  The fixed commitment of Ego at 0 can then appear as the announcing sign, "the mark in the past," of the future contingent "I retaliate at 2."

	It remains for us to show this.  We assume the problem is solved.  We thus accept that we have succeeded in demonstrating that it is rational for Ego to counter-attack at 2.  Ego, who then knows at 0 that it has a good reason to retaliate if attacked, can form the intention to do so, and express it in the form of a fixed commitment.  Alter Ego is deterred from attacking, but not entirely.  There is a small probability that it decides to do so anyway, in which case, by hypothesis, Ego retaliates.  This scenario can be written (supposedly on the Great Scroll, with a few incoherencies due to noise) thus:

	(13)	Proba(Ego retaliates at 2        Alter Ego attacks at 1)=e

where e is a positive number near zero, and the symbol A      B designates the counterfactual event: "If A were the case, then B would be the case."

	If we did not open the door to error, the probability written at (13) would be, in projected time, equal both to 1, due to temporal consistency (Ego cannot retaliate if Alter Ego has not attacked), and to 0, due to rational anticipation.  Thus the conclusion that the antecedent, "Ego retaliates at 2," cannot appear on the rational path.  In occurring time, since the event "Ego retaliates at 2" is after the event "Alter Ego attacks at 1" and therefore cannot affect it, the same probability is equal to Proba(Alter Ego attacks at 1), or 1, since the rational path then has it that the failure of deterrence is certain.  It is thus intriguing, to say the least, that, in the scenario we are describing, this number is small, near zero.  Yet the interpretation is easy, as soon as one undertakes the very special intellectual gymnastics that projected time requires.  Whatever happens, Alter Ego knows that it is written that Ego will retaliate - even if Alter Ego, by refusing to take the first step, does not give it the possibility of acting.  In spite of this, these is a chance, e, that Alter Ego will attack.  There are thus two paths which get mixed up in the script, each of which violates one of the two conditions defining a rational path: temporal consistency and rational expectation.  These two paths have one thing in common: in both cases, it is written that Ego retaliates at 2.

First Path

Second Path

	The first path, which has the highest probability, is the one most likely to shock us even though both paths, resulting from errors, appear irrational.  This writing in time of a future contingent, in spite of the fact that its first condition for possibility is not met - namely that the sequence of actual events leads to it -, irresistibly brings to mind Voltaire's criticism of the Leibnizian theodicy.  Yet this is the price which must be paid to salvage the effectiveness of deterrence.  In this respect, the tragic recent events at Waco, Texas provide a surprising illustration of my claims here.  Holed up in its bunker, the "Davidian" sect of David Koresh had repeatedly expressed, in the form of threats, its intention to liquidate itself through collective suicide.  There was all the more reason to take the threat seriously because Koresh, in his fanaticism, was convinced that it was written that the event would come to pass, whatever else happened.  Following a confusion, the F.B.I. attacked, setting off the cataclysm.  In a self-critical moment, the Attorney General Janet Reno said, so very meaningfully, "If we had known things would turn out this way, we certainly would not have attacked."  What was required was knowledge of a future event, knowledge which would have caused reactions preventing that very event, in order for the deterrence to be effective.  Janet Reno concluded: "We have made a big mistake."

	We are not yet finished since we must still show that this altered script can truly constitute a rational path.  In other words, we must show that Ego can consider it rational to form the intention to retaliate, to commit itself in a fixed way to reprisal, and to do so effectively if it is nonetheless attacked.  All that is needed to settle this question is to calculate expected utilities - a calculation which is strictly meaningless in the orthodox world because, for it, the uncertain has no place in determining the equilibrium.  The above script gives Ego an expected utility of: (1-e)-eN, or approximately 1-eN, against 0 if Ego renounces deterrence.  Deterrence is thus rational and possible, and almost certainly effective so long as eN is less than 1.

	Orthodox theorists themselves use what they call imperfect information to resolve problems which seem to them otherwise insoluble.  We have mentioned one example related to the deterrence game with a finite number of rivals (the notion of sequential equilibrium).  This imperfection is obviously of a very different nature than that of the one we have just put into play since the former is placed in occurring time.  One of the marks of this difference is very revealing.  The orthodoxy needs this imperfection to escape the trap of the equilibrium of backwards induction, both in the case of the threat and in that of the promise (an example of this is the prisoner's dilemma repeated a finite number of times; see Kreps et al., 1982).  We have had no need to introduce imperfection to save the credibility of the promise.  We have thus brought out a fundamental difference between threats and promises which the orthodoxy does not allow itself to see.  Deterrence is affected by a discontinuity which has no equivalent in promising.  Between perfect deterrence and imperfect deterrence, there is an abyss: the former self-refutes, the latter can be effective.

5.	Conclusion: From Instrumental Rationality to Practical Reason

	5.1.	The point of view on rationality which we have adopted until now is in principle the only one which the rationalist paradigm recognises .  In the decision theory proper to economics, in game theory, or in analytical philosophy of mind and action, instrumental rationality, the rationality of means and ends, holds sway.  In order to solve the paradoxes which confront this rationalist paradigm when it faces the problems we have discussed, we have nonetheless tried to save and found the so-called "evidentialist" rationality of choice.  This rationality of choice differs from orthodox rationality in that it violates Allais's principle, in other words, the principle of the fixity of the past with respect to free action.  It implies another relationship to time than the one the rationalist paradigm takes to be obvious.  Along the way, we have discovered that this "projected time" corresponds to an authentically human experience of time, linked to an ethical attitude.  What we mean by this is the attitude consisting for the subject or agent in voluntarily submitting herself to the transcendence and universality of a rule which she has instituted herself by giving it to herself.  This attitude is fundamentally different from that which consists in "tying one's hands."  Far from being a self-interested alienation of freedom, it is the assertion of the highest liberty in the form of the autonomy of the will.  Thus we may question the relations between ethics and instrumental rationality.

	In the history of moral philosophy, two opposing answers to this question can be found.  Teleological doctrines judge the morality of an act according to its contribution to an object considered to be the supreme good (pleasure, happiness, perfection, etc.).  The ancient moralities fall under this definition as does, among the modern doctrines, utilitarianism, the imperative of which can be expressed thus: "Always act in such a way as to contribute through your action (or the rule of your action) to the maximisation of the happiness (or pleasure, or utility) of the greatest number."  Instrumental rationality is the form of rationality of these ethical doctrines because actions are only means to an end set up exterior or transcendant to the moral subject.  The Kantian doctrine, in contrast, is called deontological, in that it claims to release practical reason from its submission to an object of the will defined as a good, in order to establish a "pure" will, desiring itself as a will.  This is an ethics of pure "you must" or "you ought to," in which in principle nothing which makes a human a being with inclinations or interests comes into play.  The Kantian "formalism" goes in theory so far in its refusal of instrumental rationality or, more generally, of "consequentialism," that it rejects as immoral any action inspired by the prediction of its consequences even if it cannot be distinguished from the outside from a moral action.  Thus, in the categorical imperative: "Act only according to the maxim which entails that you can want at the same time that it become a universal law" (Foundations of the Metaphysics of Morals, Second Section), the "can want" expresses an exclusively formal condition: maxims which, established as laws, are self-contradictory, and not those which, under the same conditions, lead to a contradiction between the consequences of the act and what the will targets, are to be held to be immoral.  It is not certain that Kant himself succeeded in completely fulfilling this requirement, at least in the cases of the examples he proposes when he deduces particular duties from the categorical imperative.  The most famous case is that of the false promise, or promise made to gain an advantage from another with the intention of not holding it - the Peter and Mary example itself.  What would happen if the false promise maxim became a universal law?  One answer is that the very act of promising would become impossible because there would be no one left to be taken in.  Kant put this down in black and white (Foundations, idem), but strict Kantianism claims that the true reason for the rejection of the maxim of the false promise is that it is in contradiction with itself.

	These two classes of doctrine have often come into conflict with each other.  For the former, (deontological) ethics must be rejected because it is irrational; for the latter, the moral domain, insofar as it is ruled by the categorical imperative, escapes the jurisdiction of (instrumental) rationality, which knows nothing but hypothetical imperatives (if I want something, for example the good or my personal interest, then I must do this).  In the end, these crossed criticisms share one point: they despair of ever uniting ethics and rationality.  Is there no way to reconcile justice and interest, as Rousseau hoped?  Our research opens a way out: "evidentialist" rationality.  Indeed, this possesses features which make it look like a "Kantianism with a Humian face," to use the play on words with which Michael Sandel received the publication of John Rawls's Theory of Justice: a Kantianism which retains of the empirical tradition begun by Hume the attention given to the interests of the parties, interests which put them into conflict but which also incite them to cooperate.  It is also a Kantianism with a "human" face, in that it addresses itself to interested beings and not to angels.

	In conclusion, I would like to propose two supplementary illustrations to support this thesis: the prisoner's dilemma and the voter's illusion.

	5.2.	Consider the famous prisoner's dilemma, which remains the archetypal model of individualist methodology for social sciences.  Two players, Ego and Alter Ego, each have the choice between two strategies: cooperating (C) or defecting (D).  There are four possible cases, each of which gives the two players a certain result (Ego's "payoff" appears at the bottom left of each square, Alter Ego's "payoff" appears at the upper right).

The condition for there to be a prisoner's dilemma is: T>R>P>S.

	The very great majority of the philosophers interested in this structure reason in the following way.  I am Ego.  My choice should in principle depend on what Alter Ego does, but by hypothesis, Alter Ego acts independently of me and I cannot know what it does.  However, I notice that this is not important because, whatever it does, it is in my interest to defect: if it does C, to do D (since T>R); if it does D, to also do D (since P>S).  In other words, I have a "dominant" strategy: defection, for whatever the "state of the world," or, here, Alter Ego's action, I always gain more by defecting.  It is easy to see that the rationality of the dominant strategy presupposes that we accept a metaphysical principle analogous to Allais's: the principle of the fixity of the free action of Alter Ego with respect to my own free action.  If I acted other than how I act, if I were to enter another possible world (possible because I am free), Alter Ego's action would be the same as it is in our world.

	Accepting this principle, I consider it rational to defect.  Alter Ego does too, since it is in the same position as me.  We find ourselves at (D,D), which gives us each P, whereas if we had cooperated we would have each obtained R>P.  The prisoner's dilemma is a "paradox" because the two agents mutually condemn themselves, in the most "rational" way in the world, to a situation which is, compared with another possible one, less advantageous for both of them.  In the terminology of game theory, the "equilibrium" - in other words the state in which each agent has the best strategy given the strategy of the other - is unique and "sub-optimal" - another state would have been better for both.  Note in passing, as we did in the case of deterrence, that the concept of equilibrium, on which the essence of game theory, like economics, rests, and which these disciplines hold to be purely formal, is to the contrary heavily weighed down with metaphysical presuppositions.

	It is generally agreed that the prisoner's dilemma formalizes the structure of the "state of nature" as Hobbes described it in Leviathan.  The mutual blocking in the case of (D,D) illustrates the supposedly inevitable absurdity of the "war of all against all."  Hobbes wrote, "And from this diffidence of one another, there is no way for any man to secure himselfe, so reasonable, as Anticipation."  This famous passage clearly reveals the vicious relation to time which provides the foundation for the orthodox argument and which is hidden by the concept of equilibrium which compresses it into the instantaneousness of the formal representation.  The equilibrium means that the reaction precedes the action, under the pretext that it anticipates the action.  Everyone will be "right," in the deepest unreason.  We have already encountered this in the Peter and Mary example, which is in fact simply a prisoner's dilemma in which the temporal dimension has been made explicit.

	Some authors, however, have no fear of defending the cooperative strategy using the following argument.  Suppose that Ego and Alter Ego are true twins.  Even when they are separated, they know that when placed before the same problem, they will make the identical choice.  Therefore each one can reason as follows.  Whatever I do, it is highly probable that my twin will do the same as me.  Thus the only two boxes to be considered in the game matrix are (C,C) and (D,D).  The first one is preferable for me, I thus do C.  Note that this conclusion is obtained by applying to the situation the golden rule of decision theory in its original form, and that this conclusion is none other than the "evidentialist" solution.  The argument continues: we are all twins when it comes to rationality.  Whatever we do, the others will act like us because they have the same rationality as we do.  We should thus choose to cooperate.

	Can the rationality of "evidentialism" be salvaged in the present case?  Certainly not by the above argument.  In fact, it is all too easy for the orthodoxy to uncover a formal defect in it.  The orthodoxy considers that rationality is univocal, and that "causal" rationality, its rationality, is the only rationality.  When Ego takes a counterfactual turn away from the optimum strategy, nothing permits us to suppose that in this other possible world where, thus, it plays irrationally, Alter Ego does likewise.  Nothing here allows us to question the principle of the fixity of the free action of the other with respect to mine.

	Let us grant that.  Yet it must be pointed out that this argument presupposes something which we find again in the conclusion: the univocality of rationality.  All that this shows is that if this is the case, then this univocal rationality merges with the orthodox, or "causalist," rationality.  Hopefully we have shaken the faith in rational monotheism sufficiently to be able to argue in this way.  Putting ourselves in Ego's position, if I defected, it would be a sign that I am in a world in which orthodox rationality prevails.  Alter Ego would do likewise, and I would obtain P.  If, to the contrary, I cooperated, it would be a sign that I am in another world, a world in which the evidentialist choice would be considered rational not only by me, but by Alter Ego.  I would thus obtain R>P.  I should thus cooperate.  By taking this line of reasoning, Ego gives itself a counterfactual power over the free action of another.  Taking itself out of itself, it universalizes the maxim of its action in the Kantian way.  Yet we are not in Kantian morality since what interests Ego when it asks: "What would happen if my maxim became a universal law?" is not to know if it would become self-contradictory, but to know what this hypothetical situation would bring it, in terms of its self-interest.  Those with no fear of oxymoron might speak of a "Kantian utilitarianism," or in any case of a modest, interested Kantianism which corresponds fairly well to the justification people in situations with this structure sometimes, or often, give to their actions.

	5.3.	If he is coherent with himself, the orthodox rationalist can only consider "irrational" the institution on which modern democracy rests: the vote.  Suppose voters have a choice between two candidates, or more generally two options, in a single-round majority ballot.  If they are numerous, the probability that the vote of one of them will have any effect is infinitesimal.  In fact, it is equal to the probability that the votes of the others are perfectly, symmetrically divided, which very rapidly tends toward zero when the number of voters increases.  Now, the decision to go and vote leads to costs of all sorts, undoubtably low in general, but in any case higher than zero.  It is thus irrational for each individual to vote.  It is as if the voters in most western democracies, who in fact vote less and less, did not need the support of the rational argument in order to justify their lack of public spirit.  Nonetheless, the voter's illusion, when we think about it, has wider consequences and is more profound than it might seem.

	The preceding argument is nothing but one more variation on the theme of the dominant strategy, or fixity of the state of the world with respect to my free action.  It is undoubtably meaningful that its "obviousness" is less assured in the case of the vote.  Laboratory research and experiments have revealed that subjects generally have a very hard time convincing themselves that their vote has strictly no effect because they find it extremely difficult to understand that the votes of the others are fixed with respect to theirs.  In a case like that of the United States, where the immensity of the continent, the relative autonomy of the states and the fact that the election legislation in many of them permits their results to be made public even before other states have finished voting, it can happen that the Californians, for example, are still voting when the results are already in and known.  It seems clear in this case that their behavior is in accordance with requirements other than those of pure instrumental rationality.  What is most often not understood is that even when the votes of the others are not known or when the others have not yet voted, the situation is exactly the same from the orthodox point of view: each individual vote is strictly without effect.  Yet, it is the aggregation of these votes which produces the final result.  For the orthodox theorist, the high irrationality of attributing to a collective subject the will to produce the final result ("The electorate has issued a warning by answering with a small yes, full of reservations..."), only crowns the first irrationality.

	Evidentialist reasoning provides yet another way out of this dead end (Quattrone and Tversky, 1987).  Each voter can make the following argument.  Within the electorate there are many individuals who have the same preferences as me because they belong to the same milieu, have been subjected to the same influences and the same determinism, etc.  If they decide to vote, they will vote in the same way as I would vote if I decided to vote.  However, since they are similar to me, it is highly probable they will also make the same decision as me when it comes to whether or not to vote.  If I vote, thus, I will be in a world in which those who would vote like me if they were to vote, will also vote.  When I cast a ballot, I "counterfactually" commit thousands, even tens of thousands, of similar votes.  Once more, but in a particularly spectacular manner, the power we call counterfactual (here over the free action of others) seems like magic.  However, it accompanies this movement which takes the subject out of herself, and gives her the capacity to universalize the rule of her action.

	Many other problems of social and collective life could be given a similar treatment, beginning with the persistent, vital problem of financing "public goods."  The use of these goods, such as defence, security and information, cannot be exclusive because the consumption of any one person in no way reduces the consumption of the others.  If every one acted according to orthodox rationality, such goods could not be produced: no one would be moved to contribute to financing them because no one can be excluded from using them once they exist.  In terms of economics, the "free rider" is a paragon of rationality.  From this we have a situation which is absurd for all - one more to be added to the assets, or rather to the liabilities of causalist rationality - since we can assume that each individual had more to gain from the existence of the good in question than to lose by making a contribution equal to that of the others.  The ethical reflex is to ask in such cases: "You think that your contribution will change nothing in the existence and quality of the public good.  Imagine what would happen if every one thought and acted like you."  The causalist paradigm cannot make sense of such a counterfactual situation because even if the others in fact acted like me, it would obviously not be my doing - I would not be the cause, and I would not be responsible.

	The evidentialist attitude resolves a considerable number of the difficulties of collective life.  Experience shows that it is very widespread.  A great deal of arrogance and audacity are required to judge it irrational.

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