Summary

John Searle says that human beings, among other species of animals, are capable of aiming collectively at common goals--as distinct from, and alongside of, being capable of aiming at individual goals.⁽¹⁾ What he means by this, is that many instances of goal-directed behavior, among the likes of us, cannot be thought of as a summation of individual aims at individual goals. That, in other words, the enterprise of aiming collectively is irreducible to configurations of aiming individually, with knowledge that others are so aiming as well. Searle says that his confidence in this irreducibility rests on an intuition, to the effect that all analyses of collective aimings at common goals, in terms of individual aimings at individual goals, plus common knowledge of such aims, will ultimately fail. And his reason for thinking this is that each of the individual aims which makes a contribution to achieving the common goal, when there is a common goal, is derivative -- dependent for its existence on the common goal; and not the other way around.

If Searle is right, then Bayesian accounts of decision, in all their many and bewildering varieties, are misconceived, as also are the accounts of social behavior which rest on them, even as the latter aspire to the rigor of science. For these Bayesian accounts presuppose both that agents aim exclusively at individual goals, by maximizing expected individual utilities (partly through modeling the deliberations of goal-directed others precisely as they model the undirected forces of nature),whilst at the same time presupposing that it is an imperative of reason to proceed in this fashion. Thus if Searle is right, Bayesians should be unable to explain even the simplest forms of successful coordination which involve collective aims. At least, we who are goal directed should find the explanations Bayesians put forward utterly unconvincing as explanations, however we might be disposed towards them as prescriptions.

I believe that Searle is right, against the Bayesians. But whereas Searle rests his case for the irreducibility of collective aiming on the strength of an intuition, to the effect that we-intentions are irreducible to configurations of I-intentions, I propose that we instead give it more firm, scientific foundations, by identifying how reductions such as the Bayesians commend are bound to misfire when it comes to either explaining or justifying even the most commonplace successes at coordination. I propose to expose the inadequacies of the reductionist approach, and thereby to insist on nonBayesian foundations for the science of decision. I shall propose an anti-Kantian account of agency, which rejects the Bayesian foundations of game theory, which rest on the Kantian view. On the way we shall develop a new image of the prudent individual, as one who, for the sake of achieving her aims, fosters in herself (and others) the ability to see things from the point of view of those around her, particularly those with whom she aspires to coordinate. I will thus suggest that we replace Searle's vision of the (social) human being, as endowed by his biology with the primitive sense of the other person as sufficiently like himself in being a candidate for "shared intentionality", with a vision of the social being as endowed by her psychology with the capability of seeing things from the point of view of her companions, whether these are perceived as resembling herself or not.
 
 
 
 

1. Bayesian "Coordinations"
 

Bayesian foundations of decision theory aim at treating cooperative enterprises or "games", defined as ones which permit enforceable agreements amongst the players,⁽²⁾ as they treat non-cooperative games, which admit of no such agreements. And so Bayesians aim at representing collective decision making as a species of individual decision making, not as something different in kind. The goal is to reduce what may be called "collective rationality", the process of deliberating collectively to achieve agreement for the sake of coordinating action, to what may be called "individual rationality," the process of achieving decision as individuals for whom overt deliberation is a (bargaining) game of individual-against-individual, in its own right, under the larger game. The idea is to handle the overt process of deliberation as a series of strategic bargaining moves in a competitive game of individual-against-individual, which is also governed by rules specified in advance, and therefore not as the sort of thing which someone can undergo purely as a single individual. Rather than being seen as a potential means to reaching collective decision with others, and therefore as a means of forming a single but larger decision-making body aiming at common goals, the process of deliberation is conceived exclusively as a means for each participating individual to reach their individual goals.⁽³⁾ This is, for example, a goal of Harsanyi and Selten's (1988) monumental work on equilibrium selection, although as they themselves acknowledge, the goal is never reached.⁽⁴⁾

Towards its goal, the Bayesian procedure is to define a decision problem very abstractly, by its "essentials" only: preference structures, rules of play, and knowledge that these things are themselves "common knowledge" to all participating, who (incidentally) are assumed to be consummately rational beings, in possession of common knowledge of this mutual consummate rationality, as well as unbounded deductive powers. The participants are then assumed to pass from knowledge of the "essentials" of their situation, by deliberately putting to one side (if necessary) such things as cultural norms and all other common knowledge not specifically relevant to the decision problem, via pragmatic reasoning, to a solution that compels action.⁽⁵⁾ It shall be my thesis that, while the Bayesian approach expects the deliberator to be a consummate logician, as a consequence of being consummately rational, and in that regard exaggerates the human endowment, it at the same time understates her other resources.
 

2. Nash Equilibrium

The Bayesian approach to coordination (among other things) forms one stream of the so-called Nash Program, which commends solutions to dilemmas in the form of so-called Nash equilibria.⁽⁶⁾ To define a Nash equilibrium we shall need to introduce the notion of best reply. A certain option for a given player is a best reply to other players' choices, if it best advances that player's aims (in Bayesian terms, maximizes his utility), in light of the other players' current choices. Then a Nash equilibrium is a combination of plays, one from each player, such that each one is a best reply on its player's part, to the other players' choices. A Nash equilibrium point is self-enforcing in the following sense: if each player believes that the others are doing their parts in the equilibrium stratagem, then each can be certain he can do no better for his aims by unilaterally deviating from equilibrium, and so will follow through with it, without there being a penalty imposed for deviation. For each player's part in the equilibrium is a best reply for each to what the others are doing. Now an option which is a best reply to other players' choices, no matter what the others choose, is called dominant. A dominant strategy is unconditional: it is a best reply unconditionally. Solutions that rest purely on dominance considerations are thus a proper subclass of Nash equilibria.

The sticking point is that there is often more than one Nash equilibrium in typical games, none of them supportable purely on dominance considerations. For example,⁽⁷⁾ suppose you and I are each given only one opportunity to name either Heads or Tails without communicating; we win a prize so long as our selections match. The outcome of the equilibrium point Heads/Heads is just as agreeable to us as the outcome of the equilibrium Tails/Tails. The trick is to reach one equilibrium point, rather than another, without benefit of communication.⁽⁸⁾ The naive Bayesian approach, which simply directs its adherents to maximize individual utility, without giving further instructions in the matter, does not provide a mechanism for deliberating among competing equilibria, so does not prevent miscoordinations.

There is now a very large literature attempting to refine the Nash equilibrium concept, so that the refinement will both (1) eliminate intuitively incorrect equilibria,⁽⁹⁾ and (2) leave only one equilibrium left standing as an option. For it was once thought that, if there is one unique equilibrium point, every theory, no matter its foundations, can embrace it as the solution to the game, since it has no competitors.⁽¹⁰⁾ This is quite problematic, as it simply and unceremoniously postulates that all coordination problems possess a solution, no matter how we conceive of solutions. If we are Bayesians, it would imply that every coordination problem possesses a solution that can be supported on individual utility-maximizing grounds. While there are at the same time reasons for embracing the contrary of the existence postulate.⁽¹¹⁾ Michael Bacharach, who is perhaps the only person to axiomatize what may plausibly be called "the theory of noncooperative games" as practiced in the 1980's, has proved that a Bayesian theory without principles of deliberation beyond "Maximize!" does not have solutions even to games with unique Nash equilibria.⁽¹²⁾ The ground of this proof is captured in an argument, put forward independently by Margaret Gilbert, against use of a salient property of a strategy combination (a property which allows that combination to draw prominent attention to itself as unique, and thereby to stand out as special) as potentially identifying that combination as a unique solution. The argument, in effect, is that even in the presence of a salient strategy combination, there is still nonetheless no reason for one player to believe that his own partners or opponents will or are likely to perform their parts in that combination.⁽¹³⁾ So if there is no reason for me to think you will choose your part in that prominent combination, I have no compelling reason, not even on grounds of maximizing utility, to choose my part in it. And so prominent considerations are not rationally compelling in the way they need to be in order to qualify as solutions.

One promising new approach is the idea that dilemmas ought be individuated also in terms of initial beliefs, that these enter into the "essentials" of a decision situation. Brian Skyrms has perhaps the most prominent proposal, as well as the best worked out, along these lines, but Cristina Bicchieri has another.⁽¹⁴⁾ The idea is that, in order to achieve a specific enough definition of a dilemma to reach a compelling solution, we must model also the knowledge of players, as to how they assess the other players are initially likely to play, and also to update systematically their opinions of each others' opinions, iterating the updating process until there is convergence.

The results of this approach are in fact interesting, but, as I now suggest, they are also of limited use. The problem with the idea is that it is still too narrow. For the only factors it will allow as relevantly discriminating between one dilemma and another, are ones which impact players' initial assessment of each other's likelihood of pursuing the options open to.⁽¹⁵⁾ These are prior probabilities, or simply priors (as they are known to friends and enemies alike). Allowing priors to individuate between games may be in keeping with the Bayesian program, but it runs into the following, fundamental, difficulty. If players fail, for whatever reasons, to form priors, or simply fail to form them in a way which is not commonly known to be common knowledge, then such factors as would otherwise seem relevant cannot be used to discriminate one dilemma from another. And so the Skyrms proposal will apply only if factors that otherwise seem relevant to individuating one dilemma from another, also show up as making an impact on priors. So the proposal will succeed only if players have at least comparative opinion of each proposition to the effect that the opponent will do such-and-such, that these opinions are common knowledge, and that it is also common knowledge that players update this opinion systematically, according to some definite (and possibly also defensible) rule. But this is a tall order, even when a salient solution is known to be salient. For example in our Heads-Tails dilemma, each player might know that heads has a psychological first place for the normal citizen, without having any reason to think that the opponent is more likely to choose heads (Gilbert's point again).

3. Dependent Coordinations: An Anti-Kantian Proposal

Kant, as is well known, put forward the proposal that autonomy is a property of the rational will. Others, in the same spirit, have argued that it is self-contradictory to say of a nonautonomous will that it heeds reasons, and so is rational, since a nonatonomous will does not direct itself but takes direction from another agency (someone or something in authority over it), and so has no use for reasons.⁽¹⁶⁾ Now it is this idea, that a rational individual is not one who is moved externally, on which rests the Bayesian presumption that an agent requires positive reasons in favor of one course of action over against another, and so requires a deduction of the solution to a dilemma. And this is the presumption I wish to challenge, by claiming that we do not always require reasons.

When two friends lose each other in a crowd, how do they proceed to find each other again? As we may say, it depends. For the answer to their problem cannot be reached a priori, but depends on the nature of their venture up to the point of getting lost. Each might find herself heading towards the point of initial meeting, if that is sufficiently close by. Or towards the destination point of their journey, if that is closer. Or some intermediate point, if it exerts more pressure on each of their sensibilities than either of the first two options. But if I lose my toddler, or my dog, on the other hand, I do not return to a departure or destination point, nor do I direct my path towards a prominent intermediate point, but instead seek out wandering places likely to attract the attention of a toddler or dog.

I will draw two morals from these contrasting examples. The first: whether they succeed in coordinating or not, the friends choose as they do partly -- but only partly -- because the option each chooses enjoys a psychologically more prominent position on their spectrum of perceived options. But it is the rest of the story as to why they choose as they do which is most interesting, philosophically speaking. I propose to tell it as follows: When faced with a prominent strategy, among many other things, under circumstances when coordination with others is required, individuals often themselves in possession of an impulse to act according to the prominent strategy. This impulse is a species of compulsion rather than a species of reason, which nevertheless admits of being either overridden or bypassed under appropriate conditions, as well as it admits of being complied with. In other words, I propose to understand certain features of circumstance as exerting an external power on agents, which give rise to conditional impulses to act. The properties of circumstance can give me, not a reason for acting, but instead an impulse towards a certain action or stratagem -- an impulse whose force can be measured against that of reasons, as well also as against that of other impulses.⁽¹⁷⁾ Thus when lost from you my friend, I am moved to choose a prominent point not because I have reason to believe you will choose it, or a reason to believe you will think I will choose, or anything of the kind -- although after the fact I am entitled to say that I believed you would do likewise because you had the same perspective on our situation. I choose my course of action simply because the point of reference exerted a certain pressure directly on my will, which I can elect to resist. I received from it an impulse to act -- an impulse which deserved compliance because I had no reasons to override it.⁽¹⁸⁾

The second moral I wish to draw from my examples concerns the differences when it comes to coordinating with a toddler or pet. I give in to the impulse to seek you at a place which is prominent for me, on grounds that I have no reason to believe that if I took your perspective, I would be choosing differently. This is not true when it comes to losing my son. I must bypass the impulse I receive, as myself, in that case. And I must take his perspective. I neither model him as a maximizer of utility, just like myself, nor as a duplicator of my reasoning processes -- although my son is surely both, at least on many occasions. Instead I try to imagine the situation from his point of view, to take his perspective on the situation, confident that he is positively not perspective-taking himself. Perspective-taking is not the same thing as modeling the other after yourself-as-a-rational-being, although in the case of the two friends, the two enterprises are indistinguishable in their results.

I am therefore recommending perspective-taking, in the name of prudence, not (as the Bayesians counsel) the modeling of others after self-as-rational. Perspective-taking is what is called for when I seek to coordinate with my son; indeed I would and should be faulted for modeling him after myself. So why suppose it should not be required also when I seek to coordinate with my friend? And I am also explaining the significance of salience considerations for coordination. On my account, two friends who aspire to coordinate for the sake of being reunited, should not choose purely on grounds of prominence, or even on the assumption that the other (like self) sees a certain option prominently; I agree with Gilbert, that prominence is not enough as a reason. I am instead recommending the prominent solution precisely in those instances in which the prominent solution gives rise to the same impulse to act in all would-be coordinators, an impulse that is not overridden but instead reinforced through perspective-taking. Thus the grounds on which I say coordination is achieved are precisely those on which it is permitted by prudence: coordination rests, not purely on reasons, but on a combination of reasons and impulses.

The moral of my examples is therefore a caution against embracing Kantian autonomy unconditionally, as a precondition of rational decision making. It directs against using individual, utility-maximizing rationality as the sole grounds for commending a solution to players in a dilemma, and it rejects also the Nash equilibrium as a necessary property of a solution, much less a sufficient one. Thereby it opens the door to the possibility for utilizing such things as the Pareto Principle, which recommends replacing one strategy combination, however arrived at, by another which is preferred by some party but not dispreferred by any party to the problem. I have not -- and will not -- argue for the legitimacy of other principles at this time, as it would stray too far from the main point. Simply, I suggest that once the door to impulses is open, such things as the Pareto Principle might walk in, bidden or not, if only on its credentials as a prominent idea which may give rise to impulses to act.

But a Pareto Principle is legitimate only if the enterprise at hand is viewed by those viewing it at least partly as collaborative, and not strictly as competitive. For, as Harsanyi and Selten are quite right to point out, it is a principle of what may be termed collective rationality. So if it is ever not imprudent to give in to an impulse to apply a Pareto Principle, then surely not all prudent decision-making can be viewed, even from a normative perspective, as the result of individual efforts summed "linearly" (as it were). Instead, coordination might be the result of collaborative effort, thought of not simply as resulting from communication, but resulting also from each member of the effort taking the perspective of everyone else -- or, better, the result of everyone taking a group perspective. By taking a group perspective, an individual is not acting autonomously, for she is taking guidance also from the aims of other, whether she embraces them herself or not. This is an Anti-Kantian proposal.⁽¹⁹⁾

I am thus suggesting that we need a theory of decision which individuates dilemmas also according to the relevant impulses at play, however they happen to arise, and with their proper disposition -- whether they ought to be complied with or resisted. It will be a decision theory that does not place such a great premium on individual rationality, but might possibly also save an important place for group rationality and common aims to play, as common, in giving rise to legitimate impulses to act upon.

Thus John Searle's intuition, to the effect that many instances of goal-directed behavior, among the likes of us, cannot be thought of as a summation of individual aims at individual goals -- that, in other words, the enterprise of aiming collectively is irreducible to configurations of aiming individually, with knowledge that others are so aiming as well. But whereas Searle rests his case for the irreducibility of collective aiming on the strength of an intuition, to the effect that we-intentions are irreducible to configurations of I-intentions, I am suggesting we ought to embrace the irreducibility thesis because the metaphysics of atomic-level explanations, together with the proposal that the atoms are independently moved, is inadequate to treating such things as what two friends, separated in a crowd, ought to do in order to be reunited, or what a parent ought to do for the sake of reuniting with a small child.

Searle's insight, with which I am in complete agreement, is that we-intentions can be more fundamental, metaphysically speaking, so that they give rise to I-intentions, and are not merely the sums of I-intentions, conceived of as primary and not derivative. In other words, that we-intentions can emerge from the primordial psychological ooze as we-intentions proper, standing on their own two feet as it were. And that I-intentions can be dependent upon we-intentions in an important metaphysical sense, as they flow from them. The idea being that, when two of us favor a coordination, and each knows of the other's favorable view of coordination, and each approves of the other's favorable view, and each knows of the other's favorable view of the favorable view, and so on -- then each of us is in the best possible position for forming, on impulse, a we-intention, as such -- an intention to act in concert with the other rather than to act unilaterally, to act as part of a larger action-taking body;⁽²⁰⁾ only subsequently and derivatively does this intention proceed to give rise to I-intentions to do one's part in the collaborative enterprise. From this we-intention can flow a reason for acting in one particular way rather than another (for example, of choosing an equilibrium point which awards each of us more than any of the other equilibrium points), or if conditions favor it, an impulse towards a certain action. Provided there is no countervailing reason (or impulse), the I-intention in that instance will carry the day. And this proposal, on my view, is the only one that can account for the commonplace coordinations that a Bayesian account cannot explain.

What a we-intention does, subsequent to its formation, is to correlate the behaviors of collaborators, by giving rise to coordinated impulses for action or reasons to act.⁽²¹⁾ This is how it functions to serve the interests of coordination. Thus, metaphysically speaking, what a we-intention does is reduce the number of degrees of freedom in, for example a two-by-two decision problem, from two degrees to one.

Ordinarily, when each of N persons has a decision to make, which impacts also what each of the other N-1 persons will receive as a result of these N decisions, there are N degrees of freedom in the situation, one for each decision maker. If the parties to such a decision problem seek to coordinate their behaviors perfectly, they will seek to choose as if they were a single entity, so that the number of degrees of freedom is reduced from N to one (and thereby the potential for error is also reduced). This, at least, is what happens in the ideal cases, when the attempt to reduce degrees of freedom actually succeeds. When a group of N voters each has to cast a vote for one of two candidates, and there are two political parties each sponsoring a candidate, and there is widespread party loyalty, then efforts will be expended to reduce the number of degrees of freedom from N to 2. These efforts might not succeed entirely.
 

4. The Work of Reducing Degrees of Freedom

Reducing degrees of freedom is a piece of social engineering. As such it typically takes hard work on the parts of those who wish it done. The attempt can go wrong in many ways, many more ways in fact than it can go right. But it can also go right in a number of ways, as I wish now to illustrate.

When two separated friends seek to coordinate their actions for the sake of being reunited, they seek to act collaboratively. When they do, they reduce the number of degrees of freedom in their decision problem from 2 to 1, by sharing (as I will call it) the remaining degree of freedom; they seek to act as if the two of them were each one half of a single decision-making unit. They seek for their choice to be conditioned by the choices others make; they seek to make their selection dependently, or nonautonously, in ways that Kant could never approve. By the same token, when I seek to be reunited with my lost toddler, who himself seeks to be found, we too seek to act collaboratively. And when we succeed in our effort, we reduce the number of degrees of freedom in our decision problem from 2 to 1. However, in our case we do it not by sharing the remaining degree of freedom equally, as friends equal to each other in strategic maturity do. Instead I, as the parent, relinquish any claim to a portion of the degree of freedom we aspire to share, to my child, who inadvertently, by default, claims it all for himself. For he cannot act as if one half of a single decision-making unit, due to his extreme youth. His claim to the whole of the single degree of freedom, though not unchallenged by my claim to it, nevertheless overrides mine. His deficiencies give him first title to it. This too is an idea that has been brilliantly discussed by Schelling, when he tells us that formidable capability does not always translate into advantage, and weakness can offer many protections as well as advantages. For example, a nation state unable to stabilize its economy is in a position to "command" economic assistance it might otherwise be denied, and a weak intelligence can offer immunity from threats.
 

5. Metaphysics Against the Bayesian

The Bayesian agent is a consummate intellectual. His actions are based on reasons that have a foundation entirely in his corpus of beliefs. Agency, on the Bayesian account, consists of principles of choice applied to a corpus of belief; thus the whole business can be transacted propositionally, abstracted from the moral flesh and its waywardness. It is this intellectual approach, rather than the form of principles selected for it, which I am suggesting is mistaken. We cannot expect a purely intellectual system to perform as humans do, on grounds that intellectual systems always act independently, while flesh and blood can form nonintellectual alliances as well as intellectual ones -- the flesh is subject to bonds which allow separate agencies to coalesce as their aims coincide. (This feature of my proposal therefore serves the foundational needs of classical economics, which is concerned with economic classes and their responsibilities for disposing of economic surplus, far better than the Bayesian foundations suggested by John Roemer.⁽²²⁾)

The ability to view matters from the point of view of someone else is not a purely intellectual enterprise, although it has its intellectual elements. It requires psychological capacities. No human knows what it's like to be a bat, and this reality is not due to purely intellectual deficits on our part: we simply do not have the right equipment to exercise, well or badly. For the knowledge in question is not purely intellectual. To know what it's like to be a bat, one must be in a position to experience the type of impulses a bat experiences, and this is only a small part of grasping the agency structure of a bat. The Bayesian proposal, to model others, as well as oneself, through propositions, therefore misrepresents the metaphysics of agency, simply by taking it off stage. I propose that the metaphysics of agency is central to understanding the successes of coordination, and so is central to understanding the nature of agency.
 

6. The Metaphysics of Agency

My proposal so far seems afflicted with contradiction. There appears to be a confusion of freedom with nonfreedom. When I say that parent and toddler share a degree of freedom, I give it to toddler not parent, on grounds that the toddler has a certain handicap, due to tender age, and therefore claims full title to the degree of freedom, while the parent by contrast is in possession of a capability the toddler does not have. To answer this criticism, I shall have to discuss the metaphysics of freedom, in my sense of the term.

Freedom, in my sense, is not simply the capacity for putting some plan into action. If it were, there could be no reductions at all in degrees of freedom among full-fledged agents. Freedom in my sense -- which is a sense borrowed partly from physics -- is the absence of constraint. Lack of discipline (which is the toddler's handicap in our example, come by honestly through simple youth) gives one a claim to a degree of freedom. Whereas the ability to comply with an imperative, or to advance an aim, is no credential whatever, and is instead a counter-credential. For such an ability is precisely what I have in mind by constraint on action. It does not disqualify something's being my action, that I brought it about through following an imperative or seeking a particular aim, nor does it count against its being under my control, but it does count against my title to a full degree of freedom. When we count the number of degrees of freedom in a social system, we are not looking at the capacities for action on the parts of social players. We are looking, instead, at the number of uncontrolled "dimensions" of action which can swing the social system towards one set of behaviors rather than another. Contrariwise, the degree of control in a social system is directly proportional to the level of social functioning within that system, which depends on the capacities for social functioning being exercised.

Reduction in degrees of freedom occurs among individuals with the capacity to see things from the point of view of others within the group. (But I do not claim that such a capacity is either necessary or sufficient for reduction in degrees of freedom.) And now we can see why the ability to see things from the point of view of others can help in reducing degrees of freedom: it helps with reducing the number of uncontrolled factors in the social system. When I look at things from the point of view of my toddler, I short-circuit the uncontrolled factors which arise from my own impulses, and allow his impulses to propel the social "system" towards the (in this case common) goal. Similarly when two political parties are vying for votes, the ability to see things from the point of view of others, either those in one's party or those in the other, enables one to disseminate the sort of information that will create the sorts of impulses to vote one wishes to be created.
 

7. A Standing Objection

Only individuals choose and act. Collectivities, as such, neither choose nor act and analysis that proceeds as if they do is not within the accepted scientific canon.⁽²³⁾

It is no small minority that will press Buchanan's criticism that collectivities, as such, do not act, on grounds that collectivities, as such, have no preferences or wills. I reply that my account does not require that collectivities be possessed of preferences at all, or of collective wills as such.⁽²⁴⁾ My account requires only that the action of different wills be correlated, dependent. This correlation is the result of such engineering as I described in the last section. And the idea that social engineering can reduce the number of uncontrolled social factors, which determine the dimensions of action in a social situation, is not at all problematic. In fact, the action of two wills can be correlated even if each randomizes, say, on the results of a coin toss, so long as it is the same coin which determines the result.⁽²⁵⁾
 

Notes

1. "Collective Intentions and Actions," in Intentions in Communication, P. Cohen, J. Morgan and M. Pollack, eds. (Cambridge: MIT Press, 1990), 401-415; reiterated in The Construction of Social Reality (New York: Free Press, 1995), 23ff.

2. The original classical definition defined them also in terms of the permissibility of communication; this has come to be seen as both unnecessary and counterproductive.

3. J. Buchanan, "Constitutional Economics," in Eatwell, Milgate, and Newman, eds, The New Palgrave: A Dictionary of Economics (London: Macmillan, 1987) 585-88, is perhaps most eloquent on the reasons: "Only individuals choose and act. Collectivities, as such, neither choose nor act and analysis that proceeds as if they do is not within the accepted scientific canon."

4. A General Theory of Equilibrium Selection in Games (Cambridge: MIT Press, 1988). In the Postscript they write (p. 356): "This means that our theory uses two independent, and ostensibly very different, criteria of rationality. One of them, risk dominance, is based on individual rationality: it is an extension of Bayesian rationality from one-person decisions to n-person games involving strategic interaction among n players, each of them guided by Bayesian rationality. . . In contrast, payoff dominance is based on collective rationality: it is based on the assumption that in the absence of special reasons to the contrary, rational players will choose an equilibrium point yielding all of them higher payoffs, rather than one yielding them lower payoffs. That is to say, it is based on the assumption that rational individuals will cooperate in pursuing their common interests if the conditions permit them to do so."

5. I will not survey the variety of solution concepts here, as it will take us too far afield. Suffice it to say simply that all solution concepts so far proposed, with the possible exception of correlated equilibrium, have had the minimum property of being Nash equilibria. A very sophisticated treatment of this issue is Michael Bacharach, "A Theory of Rational Decision in Games," Erkenntnis 27 (1987), 17-55.

6. This understanding of the Bayesian project results from recent harmonizations of classical game theory, with the Nash equilibrium solution concept at its core, and the Bayesian imperative to maximize individual utility, by R. Aumann, "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica 55 (1987) 1-18, and B. Skyrms, The Dynamics of Rational Deliberation (Cambridge, 1990).

7. This, and many other similarly compelling examples, first made appearance in Thomas Schelling's pathbreaking work, The Strategy of Conflict (Harvard University Press, 1960).

8. In an important sense, communication does not really help. For if I am allowed to tell you (but not show you) that I am selecting Heads, how exactly does this give you a reason to choose Heads yourself?

9. I shall not address the problems raised under this head.

10. The monumental Harsanyi and Selten (1988), op. cit., for example, rests on this idea, as do many other refinements of Nash equilibrium.

11. Robert Sugden refers to it as the Principle of Rational Determinacy in "Rational Bargaining," in Foundations of Decision Theory, M. Bacharach and S. Hurley, eds (Cambridge: Blackwell, 1991).

12. "A Theory of Rational Decision in Games," Erkenntnis 27 (1987) 17-55.

13. "Rationality and Salience," Philosophical Studies 57(1989) 61-77.

14. B. Skyrms, The Dynamics of Rational Deliberation (Cambridge, 1990); J. Harsanyi, "The Tracing Procedure: A Bayesian Approach to Defining a Solution for n-person Non-cooperative Games," International Journal of Game Theory 4, 61-94; C. Bicchieri, Rationality and Coordination (Cambridge, 1993).

15. The same holds true also of Bicchieri's distinct proposal (1993, op.cit.), although she does not employ priors as such.

16. Many have disagreed with Kant on this matter. Feminists, for example, disagree among themselves over whether autonomy is in any respect desirable, and whether women in particular ought to achieve autonomy wherever this is possible. There are feminists who believe that the trouble with autonomy is that women do not enjoy enough of it in real life, others who take a dim view of autonomy on grounds that it is tainted with (unworthy) masculine ideals, and still others who believe that autonomy is all too often confused with (both unrealistic and undesirable) separation from other human beings. See Christine di Stefano, "Trouble with Autonomy: Some Feminist Considerations," in Feminism, Susan Moller Okin and Jane Mansbridge, eds. (Vermont: Edward Elgar Publishing, Ltd., 1994), 383-404.

17. This solves Gilbert's (1989) problem (op. cit.), by rejecting the proposition that only a reason for action can rationally justify a piece of behavior on grounds of prudence, and embracing instead the proposition that compliance with certain impulses is permissible so long as no compelling reason is raised against.

18. This idea has some affinities with Aumann's notion of correlated equilibrium, although it admits as solutions strategy combinations, such as for example dominated strategy combinations, which Aumann will go to some lengths to rule out.

19. The Kantian proposal, on the other hand, involves an irresolvable tension (as Kant himself saw clearly) between persons as totally autonomous, and persons as dependent on biological bodies which are subject to all manner of external influences.

20. Bicchieri, op. cit., views this iteration of knowledge and approval as an idealization, which may not hold good when we move away from a single decision maker. I view it as a perfectly reasonable and nonidealizing, since each individual is undertaking it, at this stage, from the point of view of a single decision-making body. But I agree it is quite an idealization if the individuals undertaking it are Bayesian atoms.

21. Here is where my view comes close to the idea offered by R. Aumann, op. cit., although, as I say, he does not give it the wide application I shall do; nor does he use the concept of correlated action to replace the need for priors.

22. Analytic Foundations of Marxian Economic Theory (Cambridge University Press, 1981); "Methodological Individualism and Deductive Marxism," Theory and Society 11 (1982) 513-20.

23. J. Buchanan, "Constitutional Economics," in Eatwell, Milgate, and Newman, eds, The New Palgrave: A Dictionary of Economics (London: Macmillan, 1987) 585-88.

24. M. Gilbert, On Social Facts (London: Routledge, 1989) is prepared to give an account of collective desires and beliefs. I am not.

25. An example due to R. Aumann, op. cit.