Rationalising Conventions

SEUMAS MILLER

R A T I O N A L I S I N G C O N V E N T I O N S

ABSTRACT. Conformity by an agent to a convention to which the agent is a party is rational only if the agent prefers to conform given the other parties conform and believes the others will conform. But this justification is inadequate; what, for example, is the justification for this belief? The required rational justification requires recourse to (a) preferences for general conformity (as opposed to merely conditional preferences for one's own conformity) and (b) procedures. An agent adopts a procedure when he chooses to perform a whole set of future actions, as opposed to a single action.

Conventions play a crucial role in human societies. Human language is conventional, as are monetary systems, methods of eating, and modes of dress. This suggests that conformity to conventions is, at least for the most part, a species of rational activity. In this paper I want to try to provide a rational justification for conformity to conventions.

An action, x, is prima facie rational if an agent, A, has a preference for some state of affairs, S1, and believes that performing x will bring about S1. He prefers the action x to, say, the action y, if x-ing will bring about S1 but y-ing will not.

Two types of preference can be distinguished here. First, there is A's unconditional preference for the state of affairs S1 over another state of affairs $2. Second, there is A's conditional preference for x-ing over y-ing. A's preference for x is conditional on x bringing about $1.

Presumably many agents have many preferences which are not dependent on the actions or preferences of Others. However, some preferences are in this way dependent. In particular, agents involved in collective enterprises prefer to perform their contributory actions on the condition that others perform theirs. For example, it might be the case that agent A is willing to go to battle against a common enemy only if his neighbours B and C are likewise willing. In such a situation A prefers to x (go to battle) on condition B and C x. This preference is conditional. I suggest that conventions involve interdependence of action, a Agents conform on condition others conform. In that case agents prefer to conform on the condition that others conform; conventions, then, involve conditional preferences. But if convention followers

Synthese 84: 23-41, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands.

24 SEUMAS MILLER

are to act on their conditional preferences, then they need to believe that the condition of these preferences obtains. They need, that is, to believe that others will conform. So if A and B are the two parties to a convention to x, then:

(1) A prefers to x on condition B x-s. (2) A believes that B will x.

Therefore:

(3) A x-s.

This argument has led us to the existence of conditional preferences to conform, beliefs that others will conform, and a rational connection between these. It has led us in fact to a simple version of David Lewis's theory of convention and his preliminary rational justification thereof. 2

So far so good, but rational agents would still require grounds for coming to believe that others will conform. That is, a rational justification for premise (2) above is needed. As a first step to supplying a basis for the belief that others will conform, i.e., for premise (2), Lewis suggests the following argument. 3

(2A) A believes that B prefers to x on condition A x-s. (2B) A believes that B believes that A will x.

Therefore:

(2) A believes that B will x.

This is a valid argument; however it makes use of a premise, premise (2B), which stands in need of justification, and the same sort of justification as premise (2) required, viz., a basis for believing that others will conform. Clearly this recourse to higher-order beliefs is inadequate as it stands; it simply pushes the problem further back onto higher- order beliefs. But perhaps it is a useful first step in that if there are a number of orders of belief, and if bases for each of these orders can be found, then the overall case for conformity will be stronger than if there was recourse only to a first-order belief and its basis.

At any rate, Lewis supplies three possible bases for any given order of belief. The first of these is explicit agreement. A believes that B will conform because B has agreed to conform; A believes that B believes that A will conform because A believes that B believes that A has agreed to conform; and so on for any additional higher-order beliefs.

R A T I O N A L I S I N G C O N V E N T I O N S 25

Unfortunately explicit agreement cannot be the general basis for conventions we are looking for, since explicit agreements themselves pre- suppose conventions, viz., linguistic conventions.

Another basis is salience (where salience includes precedent insofar as precedent is only operating as the salient feature of some course of action). However while salience may have an important role to play in the generation of conventions, it is, as Lewis points o u t , 4 replaced by past conformity in the calculations of rational convention followers, once a convention is established.

The final and most important basis used by Lewis is past conformity. 5 Now, a rational agent is not bound by his past action; he does not think that his own past conformity is in itself an adequate reason for present (or future) conformity. 6 Thus, no rational convention follower will argue as follows:

(4) I have conformed in the past.

Therefore:

(5) I will conform now.

Moreover, if convention followers are rational and if they attribute rationality to themselves, then they must attribute it to others unless, of course, there is a relevant difference between themselves and others. But there is no relevant difference. Accordingly, a rational convention follower A will not expect a fellow convention follower B to conform in the present just because B has conformed in the past. The following way of arriving at a justification for A's belief that B will conform is thus rejected.

(2C) A believes that B believes that B has conformed in the past. (2D) A believes that B believes that B's past conformity is an

adequate reason for B's present conformity.

Therefore:

(2) A believes that B will conform now.

The argument is rejected because premise (2D) is false. Moreover by parity of reasoning this use of past conformity to justify

the corresponding higher-order beliefs, e.g., A's belief that B believes that A will conform, is rejected.

So A's preference to x on condition B x-s, coupled with A's belief

26 S E U M A S M I L L E R

that B will x, would justify A's conformity, if A's belief that B will conform could be justified or if the corresponding higher-order beliefs could be justified. But this recourse to past conformity to justify A's belief that B will conform, and to justify the corresponding higher- order beliefs, has not worked. A's conformity is then still without adequate rational justification. 7

It might be thought that our argument shows that past conformity must be rejected as part of the basis for the rational justification of convention following. However this thought is mistaken. What our argument shows is that if past conformity enters into the calculations of rational convention followers it does not do so in the way envisaged above.

But I suggest that past conformity does provide at least part of the required rational basis, s The precise way in which past conformity enters into the calculations of rational convention followers is something that will be taken up later in this paper.

We have seen that conventions involve at least conditional preferences and beliefs about the actions of others. Yet our attempt to find a rational basis for following conventions has failed. I now want to argue that in order to supply an adequate rational basis for convention following, we need recourse not only to conditional but also to unconditional preferences.

For what follows, I distinguish between a convention and an alternative to a convention. For any conventional action, x, performed by agent A, there is some action y, which A could have performed instead of x. The action y could be a conventional alternative. Exchanging dollars for goods is a conventional alternative to exchanging pounds for goods. Alternatively, y could be a non-conventional alternative. Refusing to exchange goods for any currency is a nonconventional alternative to exchanging dollars for goods. 9

Conventions involve general states of affairs in respect of which agents have preferences. There is the general state of affairs, all agents conforming to the convention to x; and the general state of affairs, all agents performing the alternative action to x, say y. Moreover, agents have preferences in respect of these general states. They prefer all x- ing to all y-ing, or they prefer all y-ing to all x-ing, or they have the same preference ranking for both general states. These preferences for general states are a species of what was earlier termed unconditional

R A T I O N A L I S I N G CONVENTIONS 27

preferences. Each individual prefers a general state of affairs indepen- dently of other agents' preferences or actions.

I suggest that these unconditional preferences for alternatives to conventions enter crucially into the calculations of rational convention followers. Assume that x-ing is the conventional action, y-ing the alternative action, and A a party to the convention. My suggestion then, is that A's unconditional preferences for all x-ing over all y-ing - a s opposed to A's conditional preference that he himself x, given the others do - is required for the rational justification of A's (and other agents') x-ing. To see this consider the following case.

A and B want to meet each other regularly but not in Canberra where they live and might be reeognised. Each prefers to go to the little-known hotel just outside Canberra to meet the other, given the other goes to the hotel. But each also prefers to fly tq Sydney to meet the other given the other flies to Sydney. A and B desire very much to meet regularly and clandestinely, and if there was no other option they would be prepared to pay the expensive fare to Sydney in order to meet. But the hotel near Canberra is a far eheaper and therefore more desirable option. It is clear that the rationally compelling option is to meet at the hotel. But this option is not rationally compelled by A and B's conditional preferences. Rather it is compelled by their unconditional preferences for the general state of affairs, viz., both meeting just outside Canberra. Again consider the other option. A and B meeting in Sydney is a conventional alternative to meeting just outside Canberra. But there is yet another nonconventional alternative, viz., each staying at his/her place and thus failing to meet. Each then prefers to stay at home given the other does not go to the hotel or to Sydney. But while staying at home would be consistent with the agents' conditional preferences, it would not be rational for these agents desper- ate as they are to see one another. Why not? Simply because their preference rankings for the general state of affairs A and B going to the hotel (or A and B going to Sydney) is far higher than their preference rankings for the general state, A and B staying in their respective (marital) homes.

It might be argued that I have shown that if there are significant differences in(unconditional) preferences for general states then these can affect the rationality of conformity to a convention, but not if this is not the case. It might then be suggested that the alternative to most conventions is an equally preferable conventional alternative, e.g., driving on the left is as preferable as driving on the right.

In response to this, first, it is clear that in general the (unconditional) preference rankings for a certain class of alternatives to conventions differ quite radically from the (unconditional) preference rankings for the conventions themselves. This is because in general conventions have nonconventional alternatives for which agents have a very low


(unconditional) preference ranking. Thus the nonconventional alternative to all driving on the left is chaos on the roads, the nonconventional alternative to exchanging dollars for goods is a return to barter, etc. Moreover even where there are no nonconventional alternatives, the (unconditional) preference rankings for the various conventional alternatives can differ markedly, e.g., in the above-mentioned meeting- place example.

Second, even in those cases where all the alternatives (conventional and nonconventional) have the same preference ranking as the convention itself, conditional preferences are inadequate to compel a rational course of action. Assume that the alternative actions are x-ing and y- ing, and that the agents A and B both (unconditionally) equally prefer A and B x-ing to A and B y-ing. (Assume also mutual knowledge of one another's rationality, beliefs, preferences, and actions.) Then helping ourselves only to conditional preferences (and beliefs in respect of same), we have:

(1) A prefers to x given B x-s.

(This is of course consistent with A preferring to y given B y-s.)

(2) A believes that B prefers to x given A x-s.

Our mutual knowledge condition yields:

(2A) A believes that B acts on B's preferences. (2B) A believes that if A x-s B will come to believe that A has

x-ed.

From (2) and (2A) it follows that: 1°

(2C) A believes that B will x if B believes that A has x-ed.

From (2B) and (2C) it follows that:

(3) A believes that if A x-s B will x,

(A similar argument can be generated from A's conditional preferences for y-ing.)

Can we conclude from (1) and (3) above that A will x? We cannot. For if it were the case that A (and B) strongly preferred the general state of affairs A and B y-ing, then the rational agent A would not x. Rather A would y, knowing that if he y-ed B would also y. The required missing premise is:


(4) There is no alternative general state, (A and B y-ing), such that A (unconditionally) prefers (A and B y-ing) to (A and B x-ing).

It might be argued that the above argument can be circumvented in such a way as to avoid the introduction of unconditional preferences. The mode of circumvention is to provide conditional preferences with rankings. Thus A might prefer to x given B x-s, and his strength of preference might be six. A might only have a preference of strength two for y-ing given B y-s. If this were the case, and assuming B had the same preference rankings as A, then x-ing would be rationally compelled. For if A in this way preferred x-ing to y-ing and knew, as he would, that B will x if A x-s, then obviously A - given he is rational - w i l l x .

The first thing to note is that this manoeuvre concedes the need to supplement any account of the alleged rational basis for convention following in terms of conditional preferences by providing the relative strengths of (what are alleged to be) conditional preferences. But, it is not the strength of (A's preference for x-ing given B x-s) relative to (A's preference for not x-ing, given B x-s) that is required; rather it is the strength of (A's preference for x-ing, given B x-s), relative to (A's preference for y-ing, given B y-s).

However, this manoeuvre in fact simply smuggles in unconditional preferences. Agent A can prefer x-ing to y-ing unconditionally or he can prefer x-ing to y-ing under certain conditions. Thus, that A prefers x-ing to not x-ing given B x-s, is a conditional preference. On the other hand, if A simply preferred x-ing to y-ing, his preference would be unconditional. Similarly, when A prefers x-ing given B x-s, to y-ing given B y-s, A's preference is not conditional. There is no condition such that A prefers one course of action over another just in case that condition obtains. Rather A has an unconditional preference; an unconditional preference for (x-ing given B x-s) over (y-ing given B y- s). But this is just to say that A prefers the general state (A x-ing, B x-ing) to an alternative general state (A y-ing, B y-ing).

The upshot of our discussion then, is that rational convention followers require recourse to their unconditional preferences in respect of conventions and their alternatives. We are now in a position to offer a preliminary account of the rational basis of conventions.

Assume that there are two parties, A and B, to the convention to x,


and that there is mutual knowledge of one another's rationality, beliefs, preferences, and actions. The argument available to A (and B) is as follows:

(1) A prefers the general state (A and B x-ing) to all the alternative general states.

(2) B prefers to x given A x-s.

From (2) and the mutual knowledge condition it follows that:

(3) A believes that B prefers to x given A x-s.

From the mutual knowledge condition it follows that:

(3A) A believes that B acts on B's preferences. (3B) A believes that if A x-s B will come to believe that A has

x-ed.

From (3A) and (3) it follows that:

(3C) A believes that B will x if B believes that A has x-ed.

From (3B) and (3C) it follows that:

(4) A believes that B will x given A x-s.

From (1) and (4) we can derive the desired conclusion:

(5) A x-s.

Moreover, from (2) and (5) it follows that:

(6) B x-s.

Thus there is conformity to the convention. In the case of some conventions, an agent cannot know in advance

of his own conformity whether the other agent(s) have conformed. The telephone paradigm is of this sort. Here the convention tells telephone users what to do when they are cut off. The convention might be to call back if you are the original caller, but not otherwise. Now if you were the original caller and you call back, you do so not knowing whether the other agent is conforming by waiting for your call, or not conforming by calling back himself.

In such cases a problem might seem to arise for our above-described rational basis. Agent A cannot conform while relying on B to see A's conformity and follow suit. But this is not really a problem since A and


B mutually know that they both overwhelmingly prefer one general state, both x-ing, over the alternative general state, both y-ing. This being so A would x rather than y, in the knowledge that: (1) B preferred that both x, and (2) B believed that A preferred that both x. Moreover A would so x notwithstanding the fact that he would not know in advance whether B had x-ed or not.

In the case of some conventions, agents may have no particular preference for one alternative general state over another; both states are equally preferred.

But this is not in itself a problem. Agent A will simply arbitrarily perform x (or y) and B will follow suit if he knows what A has done. For A does not mind whether both x or both y (and he believes B does not mind either). Moreover, A believes B prefers to x if A x-s.

A real problem does emerge however if the agents have no preference for one general state over another, and in addition it is not possible for one agent to believe that the other agent has conformed in advance of the first agent conforming himself. This might be the case with the telephone paradigm.

It is here that agents would have to have recourse to salience in the generation of the convention, and to past conformity, once the convention was established. I propose to take up the whole matter of past conformity shortly and will consider these cases in due course.

Further there are certain conventions in which there is considerable conflict of interest between agents, and this is a further source of difficulty.

Consider the case of oligopolists establishing a convention to set a higher price than would otherwise obtain. If all conform then all are better off than they would be if no one conformed. However, the individual oligopolist would be even better off if the others conform and he does not. For in that event his low price would increase his sales, and hence his profit, at the expense of the others.

Once again, I suggest the solution lies in part at least in recourse to past conformity. Accordingly, I postpone consideration of these cases.

The latter two types of case require, I have suggested, the deployment in agents' calculations, of the inductive evidence of past conformity. Moreover the rationality of even the unproblematic types of case is greatly buttressed by the fact of past conformity. And in any case, as we saw earlier in our discussion of Lewis, even apart from these considerations an account of the role of past conformity is required.


Accordingly, the task now becomes one of showing exactly how past conformity enters as inductive evidence into the calculations of rational convention followers. However to enable us to show this we first need to introduce some distinctions and deploy them in our account of conventions.

For the purpose of what follows I introduce a distinction between regularities (in action) and what I will call procedures.H

In the case of a regularity in action an agent provides himself (or could do so) with a reason for performing the action he regularly performs, and does so (or could do so) on each and every occasion of his performance of that action. Moreover, the reason in question justi- fies that action considered on its own. The existence of such a reason (or perhaps reasons) means that there is (or could in principle be) a new decision to perform the action on every occasion on which it is performed. There is, if you like, one decision for one action.

In the case of procedures, by contrast there is a single decision to perform many actions. The agent decides at time tl that he will perform an action (of type) x at time t2, and also perform x at times t3, t4, etc. One decision then - the decision to adopt the procedure - governs a whole set of future actions. One process of reasoning will take place, namely that justifying the adoption of the procedure. Thereafter the agent will not provide himself with a reason for acting, he will merely identify the situation as being of the sort for which he has adopted the procedure in question, and then simply follow the procedure, perform the action.

The basic characterisation of procedures then, is in terms of a set of actions governed by a single decision, as opposed to a set of actions each member of which is governed by a different decision. However, procedures involve some additional characteristics.

In the case of an ordinary nonprocedural action, the agent decides to perform the action and immediately performs it (other things being equal, e.g., there being no outside interference). There are cases, however, in which an agent decides today to perform an action tomor- row. In that case there is time for him to reverse his decision. Let us call such decisions reversible. Now the decision to adopt a procedure, a whole set of actions, is a species of reversible decision. For many, though perhaps not all, of the actions thus decided upon may fail to be performed as a result of a reversal of the original decision. Let us call


such a decision partially reversible. Moreover, unlike ordinary decisions, there is a clear sense in which decisions to adopt procedures can be partially enacted. Some members of the set might be performed, but not others, due to a reversal of the decision.

Further, the set of actions thus decided upon is open-ended. This is because the decision to adopt a procedure is a decision to perform a type of action in a certain type of circumstance, indefinitely into the future.

Finally, the decision to follow a procedure is conditional. The condition is that the basic purpose for following the procedure has not ceased to exist. There are in addition some procedures the following of which is conditional on others following them. Conventions are of this sort. Of course in general at the time of adoption this (or these) condition(s) will have been met, but it (they) may cease to be met at a later date. Moreover, because the decision is partially reversible, it can be conditional in this sense. (It should be noted that given that the decision is conditional, ceasing to perform the relevant action when one of the conditions is not met, is in one sense not a reversal of the original decision. But I use the term reversal in such a way that a case like this would be a reversal.) Thus procedures involve a single decision to perform a set of actions, yet they involve a partially reversible, partially enactable and conditional decision, and an open-ended set of actions.

It is important to note that while the property of conditionality does to some extent qualify the sense in which a procedure is a single decision to perform a set of actions it does not negate it. For in the first place our definition of procedure is such that it is not the case that in every instance of a situation covered by a procedure a new decision to perform the requisite action type could be made after a process of adequate reasoning. This means that the matter of whether the conditions under which the original decision was made to adopt the procedure have been met is not something that can arise on every occasion, but rather only from time to time. In the second place even in those instances in which the matter of whether the conditions have been met does arise there is no wholly new decision to perform the action type in question. For there is a presumption in favour of the procedurally determined action, a presumption which can only be offset by the nonobtaining of the condition(s). Of course, an agent could decide on a wholesale review


of a given procedure and refuse to be bound by this presumption or to restrict himself to these conditions. In that case he would indeed be embarking on a process of reasoning which would lead to a wholly new decision, and his subsequent action(s) would not in any sense be bound by the original decision to adopt the procedure in question. Insofar then, as an agent in his periodic reviews of a given procedure accepts the presumption in favour of the procedural action and merely tests the relevant condition(s), his original decision to perform a set of actions does not collapse into a series of decisions each of which govern a subset of the original set.

How could it be rational to adopt procedures rather than merely conform to regularities in action? The point of procedures is to free oneself from the need to make a new decision after a process of reasoning on every occasion of a recurring situation. Such decision making with its attendant reasoning is hugely time-consuming. Indeed, the complexity of interaction that human beings have with the world (insofar as that interaction is under their control) is so great that an agent could be attending to, reflecting on, and deciding upon only a very small number of the matters which he is in fact being compelled to deal with.

One final point about the 'decision' to adopt a procedure. The 'decision' and the process of reasoning of which it was the result may in fact be implicit in the agent's behaviour. There does not have to be an explicit process of reasoning and deciding. However, the reasoning in question does have to be at some level known to the agent. Further there has to be some point, or more likely period, before which the agent did not follow the procedure, after which he did, and during which there is evidence of some process, perhaps implicit, which could be described as in some acceptable sense a process of reasoning and of deciding. At any rate, I here simply invoke the notion of implicit states and processes, without offering a full account and justification of them.

Having distinguished procedures from regularities, I claim that conventions are a species of procedures and not of regularities in action.12 This suggestion will, I hope to show, enable us to see how past conformity enters into the calculations of rational convention followers.

If the convention to, say, drive on the left is a procedure, then how is conformity to that convention to be rationally justified? If conventions are procedures, then there can be basically three different kinds of


request for a rational justification. First, there is a request for a justification of the performance of a particular action token considered on its own. Since the action token is one of a set governed by a single decision, this request is illegitimate. There is no rational justification other than perhaps, "because the procedure is to drive on the left". Alternatively, it might be asked (though only periodically) why one ought to continue to drive on the left for the foreseeable future. Now this could be a request for either one of two things. It could be a request for a wholesale review of the procedure to drive on the left; here there is a refusal to be bound by the presumption in favour of conformity, or to restrict the discussion to whether or not the conditions upon which the original decision was made have been met. In that case, what is being contemplated is a reversal of the original decision. The other possibility is to ask whether the conditions upon which the original decision was made still obtain. In that case what is being asked is: (a) whether agents still have a preference for the general state of affairs, all driving on the left, and (b) whether agents have abandoned the procedure to drive on the left. If agents still have the same preference and have not abandoned the procedure, then the conditions of the original decision are still being met, and agents rationally ought to continue to conform.

Let us look first at the. latter question regarding the obtaining of the conditions. As far as condition (a) is concerned, since there is no special problem in knowing one another's preferences for individual actions, there is presumably no special problem in knowing one another's preferences for general states, and hence preferences for the general state, all driving on the left. By contrast condition (b) seems problematic. How does an agent know that other agents have not abandoned the procedure to drive on the left? I suggest that this is the first point at which rational convention followers need to consider one another's past conformity, and allow it to enter into their calculations. Whether or not an agent has adopted a procedure is settled (in part) by recourse to inductive evidence, and in particular the inductive evidence of past conformity. The fact that an agent has always in the past driven on the left is inductive evidence that he has a procedure to drive on the left. Moreover not only is one agent's past conformity inductive evidence for other agents, it is also inductive evidence for that first agent himself.

Let us finally consider a request for a wholesale review of the proce-


dure. Since such a request for a wholesale review rejects any presumption in favour of the previously followed procedure, it amounts to a request to supply a rational justification for the adoption of the procedure in the first place. 13 We could nevertheless distinguish between initial adoptions and readoptions; a readoption occurs after a procedure is rationally justified in a wholesale review. In the case of conventional procedures, we could speak of establishing and reestablishing.

The reasoning available to agents A and B who are considering whether to establish (or reestablish) a convention to x and who have mutual knowledge of one another's preferences, beliefs, actions, and rationality, is as follows:

(1) A prefers the general state (A and B having procedure x) to all alternative general states.

(2) B prefers to adopt procedure x given A adopts procedure x.

From (2) and the mutual knowledge condition it follows that:

(3) A believes that B prefers to adopt procedure x given A adopts procedure x.

From the mutual knowledge condition it follows that:

(3A) A believes that B acts on B's preferences. (3B) A believes that if A adopts a procedure to x, B will come

to believe that A has adopted the procedure to x.

From (3) and (3A) it follows that:

(3C) A believes that B will adopt a procedure to x if B believes that A has adopted the procedure to x.

From (3C) and (3B) it follows that:

(4) A believes that B will adopt procedure x, given A adopts procedure x.

From (1) and (4) we can derive the desired conclusion:

(5) A adopts procedure x.

Moreover from (2) and (5) it follows that:

(6) B adopts procedure x.

In the above reasoning, A and B need to believe that one another have


adopted the procedure. But their past conformity is inductive evidence that they have adopted the procedure. This then is the second point at which past conformity enters into the calculations of rational convention followers. Past conformity enters as inductive evidence into the calculations of rational convention followers not only in the periodic determining that an already established conventional procedure has not been abandoned, but also in the establishing and reestablishing of conventions.

This completes our basic account of the rational basis for convention following. However, there are some residual problems that need to be dealt with.

You'll recall that there were two kinds of case that our early model of the rational basis for convention following, in terms of unconditional preferences for actions but not procedures, failed to accommodate.

The first kind of problem arose in situations where there were two equally preferable general states, and in addition, it was not possible for one agent to believe that the other agent had conformed in any given instance of the recurring situation in advance of the first agent conforming himself. This might be the case with Lewis's telephone paradigm.

Now if conventions are procedures, then each token action considered on its own does not have to be rationally justified. Moreover, agents will be aware of one another's past actions, and current preferences. There is no special problem then in justifying continued conformity in the sense of determining whether the conditions governing continued conformity to a convention have been met. The problem arises rather in the adoption of the convention or in what amounts to the same thing, wholesale review of the convention. But on our account, agents do not need to know whether or not other agents have conformed in the present instance of the recurring situation; rather they need to know whether other agents have adopted the procedure. But this they can know by recourse to past conformity. Where a convention of the sort under discussion has yet to be established, an agent A will arbitrarily decide to x rather than y on a number of consecutive occasions. By x-ing A renders x-ing salient. Agent B will now choose to x believing x-ing is salient. At some perhaps indeterminate point A will adopt x-ing as a procedure, B will have inductive evidence that A has the procedure to x, and B will likewise adopt the procedure to x. Where it is reestablishment that is in question x-ing will already be salient,


and agents will begin by x-ing on a regular but nonprocedural basis before finally adopting x-ing as a procedure. In both the establishing and reestablishing of conventions, there is a process from salience to both adoption of procedure and mutual knowledge of adoption of procedure in virtue of the inductive evidence of past conformity. The important point however is that in neither establishing nor reestablishing do agents need to know whether other agents have conformed in the present instance of the recurring situation; rather they need to know whether other agents have adopted the procedure.

The second kind of problem that earlier arose was one where there was an element of conflict. This type of case is exemplified by Lewis's oligopoly paradigm.

The problem arises as before in the establishing or reestablishing of the convention. However, the problem we confront is once again crucially different from that confronting a theorist seeking to justify each token conventional action considered on its own. Our agents are each considering performing a whole set of future actions, and not simply a single action. Moreover our agents are considering a reversible, conditional decision. Now although an agent A's payoff is high if both he and the other agents perform the action x-ing, and fairly low if both he and they do not perform it, his payoff is even higher if they conform and he does not. Given this arrangement of payoffs then, what is required to justify adoption of the conventional procedure, x-ing? On our model, many actions, a whole set 'of future actions, are being considered. Thus, each agent thinks of one or two actions in the im- mediate future as being of no great importance. But in that case he needs to consider three apparent possibilities. First, there is the possibility of all including himself conforming in the longer term; second, of all including himself failing to conform in the longer term; and third, of all excluding himself conforming in the longer term. In fact, in the longer term, there is no possibility of all excluding himself conforming. In the longer term other agents are not going to conform in the knowledge that he is not conforming, and he knows this. The choice for the long term is thus between all or none conforming. But in that case each prefers all conforming, so in the long term a group of rational agents will conform. What then is the strategy to bring about the most desired possible state of affairs, viz., that all conform in the longer term? If A x-s a few times and others do not, A's loss will be small relative to the possible payoff if he and others adopt the procedure to x. Now A ought

R A T I O N A L I S I N G CO N VENTIONS 39

to be prepared to take the small risk of x-ing on the next few occasions of the recurring situation. For by doing so he can register a willingness on his part to x, it being common knowledge that he will not x over a long period of time on his own but ultimately only conditionally on others x-ing as well. It is mutual knowledge, in other words, that his decision is reversible and may be partially enacted. Once an agent has x-ed once 'or twice (at a small loss relative to the gain over the total set of recurring instances if both x) then the other agent(s) would be irrational not to likewise x, if he (they) has not already done so. Each instance in which all agents x increases the probability that all will continue to x. After a period of time their expectations of one another will strengthen, and finally and perhaps imperceptibly, they will adopt the procedure to x. But the decision to adopt the procedure is not irreversible; a continued conformity is conditional on others not having abandoned the procedure or changed preferences, and from time to time agents will check that these conditions still obtain.

Thus on our model, recourse can be had to the idea of taking into consideration possible payoffs in future instances of a recurring situation, and this allows us to overcome the problem posed by nonconventional alternatives for accounts which seek to justify token conventional actions considered on their own. 14

E D I T O R ' S NOTE

Our referee has called our attention to the similarity between this paper and the first (unpublished) version of Professor Margaret Gilbert's paper 'Some Limitations of Rationality', now in this issue as 'Ration- ality, Coordination, and Convention'. An abstract of this paper was published in the Journal of Philosophy in 1983. As far as we have been able to ascertain, and according to Dr. Miller, this represents a case of simultaneous independent discoveries.

NOTES

1 I have argued for the interdependance of actions performed in conformity to a convention elsewhere (unpublished material). See also my paper, 'Conventions, Interdepend- ence Of Action and Collective Ends', Nous (1986). 2 David Lewis, Convention (Harvard University Press, 1969). For criticisms and recon- structions of Lewis's theory see Margaret Gilbert, 'Game Theory and Convention', Synthese (1981); 'Agreements, Conventions and Language', Synthese (1983); 'Notes on

40 SEUMAS MILLER

the Concept of a Social Convention', New Literary History (1983); and my papers, 'Lewis on Conventions', Philosophical Papers (1982); 'Conventions, Interdependence of Action and Collective Ends', op. cit.; 'Conventions and Social Contracts', Philosophical Papers (1987). 3 For a more detailed account and criticism of Lewis's account of the rationality behind convention following see my paper 'Conventions, Expectations and Rationality', Sou- thern Journal of Philosophy (1987). 4 Convention, pp. 35-42. 5 Ibid. p. 57. 6 Unknown to me at the time of writing this paper, Margaret Gilbert had made a closely related point in an unpublished paper presented to the American Philosophical Associ- ation, 'Some Limitations of Rationality' (abstract in Journal of Philosophy, 1983, p. 615). 7 For a more detailed account of this point see my paper 'Conventions, Expectations and Rationality', op. cit. 8 I have argued for the claim that past conformity provides part of the rational justification for conformity in the case of established conventions elsewhere (unpublished material). 9 For an extended account of the distinction, see my 'Conventions, Interdependence of Action and Collective Ends', op. eit. 10 Premise (2) (A believes that B prefers to x given A x-s) is ambiguous due to the ambiguity of "B prefers to x given A x-s". The latter could mean that B's preference is conditional simply on A's x-ing, or that it is conditional on B's believing that A is x-ing. My account makes use of the latter meaning, and thus my argument requires the additional premise (2B) A believes that if A x-s B will come to believe that A has x-ed. u Unknown to me at the time of writing, Margaret Gilbert had introduced a notion related to my notion of a procedure in her 'Some Limitations of Rationality', op. tit. 12 A variety of commentators including Gilbert (cited above) have argued that conventions are not regularities in action. 13 To be more precise, it amounts to the same thing just in case all agents decide to go in for a wholesale review of the convention at the same time. In the case where it is only an individual or minority going in for wholesale review there is no real problem. The individual (or minority) has a belief based on the inductive evidence of past conformity that the majority have not abandoned the procedure; since he himself (the minority) still prefers to conform given they conform, he (the minority) rationally ought conform. ~4 Thanks to an anonymous referee from Synthese for comments on this paper.

R E F E R E N C E S

Gilbert, M.: 1981, 'Game Theory and Convention', Synthese 46, 41-93. Gilbert, M.: 1983a, 'Agreements, Conventions and Language', Synthese 54, 375-407. Gilbert, M.: 1983b, 'Notes on the Concept of a Social Convention', New Literary History

XI¥, 225-51. Gilbert, M.: 1983c, 'Some Limitations of Rationality', Journal of Philosophy LXXX,

615. Lewis, D.: 1969, Convention, Harvard University Press, Cambridge, Massachusetts. Miller, S.: 1982, 'Lewis on Conventions', Philosophical Papers XI, 1-8.

R A T I O N A L I S I N G CONVENTIONS 41

Miller, S.: 1986, 'Conventions, Interdependence of Action and Collective Ends', Nous XX, 117-42.

Miller, S.: 1987a, 'Conventions, Expectations and Rationality', Southern Journal of Philosophy XXV, 357-72.

Miller, S.: 1987b, 'Conventions and Social Contracts', Philosophical Papers XVI, 85-106.

Dept. of Philosophy Rhodes University Grahamstown 6140 South Africa

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Rationalising Conventions