Can There Be a Rational Solution to No-Communication Co-ordination Problems By Means of Salients?

Rational decision theory seeks to determine a principle by which actions ought to be judged rational. Within the literature of rational decision theory there are a number of types of hypothetical situations in which one or more persons are faced with a dilemma and are asked to choose between several possible courses of action. Some of these hypothetical situations make it necessary that the agents involved must cooperate or co-ordinate with one another in order for each to maximize his or her interests. One of the objectives of creating such situations is to challenge common conceptions of what it means to act rationally. Some hypothetical situations allow for communication between the agents involved. Hence, it might be thought that if two agents have the ability to communicate with one another, they could decide on a common course of action that would be most rational for each to pursue. Other situations do not allow for communication between agents. I will argue that in some situations of no-communication co-ordination, there may often be a rational solution to the dilemma by appealing to salience; however, salience alone does not provide a reason to act.

Before we begin, I first want to provide some background to the problem of rational decision theory. On the received view of rational decision theory, an action is believed to be rational if and only if that action maximizes one’s individual expected utility (Campbell, pp18-21). So, in order to act rationally when one is faced with a choice between two options, one must choose that option that she believes, at the time of choice, is most likely to bring about the greatest amount of utility for her. To choose an action other than one that maximizes one’s individual expected utility is to choose irrationally.

In games of no-communication co-ordination, the main problem to overcome when deciding which course of action is most rational is to attempt to determine what your opponent will do. So, for example, in the standard version of the Prisoner’s Dilemma as presented by Campbell, two prisoners have been charged with a crime. Each is given a choice: each prisoner can either confess to the crime, or not confess to the crime. If both prisoners confess, each will spend nine years in jail. If neither prisoner confesses, each will get one year in jail. However, if prisoner A confesses, but helps to convict prisoner B – who remains silent – prisoner A will not go to jail, and prisoner B will spend ten years in jail (p. 4). Depending on what the other prisoner does, confessing could result in either receiving the least amount of time in jail, or receiving a considerable amount of time in jail. Hence, any clue as to which course of action the other prisoner might choose will be helpful in achieving one’s individual expected utility. I argue that in some situations of no-communication co-ordination, salience can sometimes provide that clue to the most rational course of action. By the term “salient,” I simply mean that quality or feature of a no-communication co-ordination problem that is most prominent, or most striking, or most noticeable. In other words, the salient solution in a no-communication co-ordination problem will be that clue which is obvious, or that which “stands out” as the “right” choice.

One critic of the notion that salience can serve as a rational solution to no-communication co-ordination problems is Margaret Gilbert. Gilbert’s position on the role of salience in rational decision-making is that an individual acts blindly, not rationally, when choosing a salient solution (p. 61). Gilbert’s focus is specifically whether salience alone will generate a reason for action, or whether other considerations are needed for an action to be rational. Let us first consider an example so that we might understand more clearly what is at issue.

The following example is taken from Gilbert. Suppose two strangers, Sally Brown and Joe Smith, have both been kidnapped and put into two separate rooms, unable to communicate with one another. Let us also suppose, as is customary in game theory situations such as this, that Sally and Joe are both rational agents who have a desire to maximize their individual expected utility, and that each person knows this fact about the other. Now, Sally and Joe are each given a board with four coloured buttons (red, blue, yellow, and purple). Whenever either prisoner presses his or her button, the colour of the button pressed will be noted by the kidnapper. It is then announced over a loudspeaker that in order for each prisoner to go free, each must press the same colour button on his or her board. If Sally and Joe fail to press the same colour button, or choose not to press a button at all, both of them will be put to death. So, in order for both prisoners to escape with their lives, they must co-ordinate their actions. It is important to remember that there is no communication between the two prisoners. Suppose further that while each prisoner is sitting in their respective rooms, a radio is played over the loudspeaker, and both prisoners hear the following message:

Today is our President’s birthday. His wife is giving a party for him using red as the theme colour. Red is the President’s favourite colour. There will be red tablecloths on the tables, the waiters will wear red jackets and ties, the President’s wife will wear a red dress, red stockings and red shoes, and the food eaten will all be red: gaspacho soup, sole in a tomato sauce, and a strawberry dessert (Gilbert, p. 65).

Now it seems quite likely that Sally and Joe will, in all likelihood, recognize that red has been made salient. That is, given the fact that red has been mentioned so many times in the message, each will have good reason to think that the other will pick up on this “clue.” For argument sake, let us go so far as to say that Sally and Joe do recognize red as the salient solution in this situation. The question is, ‘does salience provide a reason for each to press the red button, given that red has been made salient?’ Gilbert does not think so.

Gilbert argues that a salient solution to a no-communication co-ordination problem does not provide a person with a reason to act. In other words, simply identifying the salient solution does not give one a reason to act on the salient solution. As Gilbert points out, even if a salient solution is recognized in a no-communication co-ordination problem, this does not give one a reason to think the other person will do her part in choosing the salient solution. In other words, salience itself does not provide a reason for action; all salience can do is show us a way in which we may choose to act in order to co-ordinate our actions. But it does not provide us with a reason to think the other will do her part in choosing the salient solution.

So let us be clear on Gilbert’s argument. Gilbert is not denying that people can and often do identify a salient solution when choosing a course of action to follow. So it is not at issue whether Sally and Joe will be able to identify red as the salient solution. After all, there appear to be clear results from a number of psychological studies that suggest that people often do identify a salient solution to co-ordinate their actions in no-communication co-ordination problems. Gilbert acknowledges as much in her paper. What Gilbert is denying is that salience provides one with a reason to act.

To make her point even clearer, Gilbert changes the original example. For sometimes, as Gilbert points out, the course of action that is salient is eliminated as an option simply in virtue of its salience (p. 67). So let us return to the example of Sally and Joe, and suppose the following announcement is made over the loudspeaker: “It is well known that Joe Smith and Sally Brown are phobic with respect to the colour red. Each will avoid choosing something red at any cost” (Gilbert, p. 67). As Gilbert points out, it now seems very unlikely that Sally and Joe will choose red, even though red is the salient solution. With this turn of events, Gilbert concludes that salience cannot provide a reason for action if it is clear that Sally and Joe will no longer choose the salient solution in this situation. But I would argue that all that Gilbert has shown is that red is no longer the salient choice due to the new information that has entered the game. In order for a choice to be salient, it has to be the obvious choice for both players to choose. Red cannot be the obvious choice for either player if it is clear that both have a phobia to the colour red. So, red has, in fact, been eliminated as a possible salient solution in this new situation. So now that we are left with three colours to choose from, none of which seem salient, the rational choice is no longer apparent. Hence, all Gilbert has shown is that salience has no role to play in the modified version of the scenario.

But let us return to the main problem identified by Gilbert, which is that there is no reason for Sally to think that Joe will do his part in acting on the salient, and likewise, there is no reason for Joe to think that Sally will do her part in choosing the salient action. As Gilbert says, “[t]he fact that a good outcome would be reached if both did something cannot by itself be a reason for either one individually why he should do it. For his doing it cannot itself ensure that the other does it” (p. 72). But I am inclined to argue that Sally could be well justified in believing that Joe will do his part, and vice-versa. With regard to the original scenario, Sally might reason as follows: First, I have to identify a salient solution. In this situation, the red square would appear to be the salient option for me, given that it has been mentioned numerous times. Second, given that I have recognized the red square as salient I am assuming that Joe will also pick up on this clue, considering that he has heard the same announcement. I am justified in making this assumption because people typically look for clues when trying to solve problems such as this. This is human nature. Furthermore, given that the other three colours have not been mentioned, they seem less likely to be chosen by Joe, because such a choice would be random, whereas we at least have some reason to choose red. Third, I also have to assume, or hope, or have a belief, that Joe will recognize the salient and choose to do his part. I feel justified in assigning a higher probability for Joe choosing the salient than not choosing the salient, because I believe that Joe wants to live. And the only way Joe can remain alive is for he and I to co-ordinate our actions.

Gilbert’s response to this line of reasoning is that we are now including “background knowledge” if we assume that the other will do their part in choosing the salient solution. But as Gilbert says, “…we are not supposing that there is any such background knowledge” (p. 66). But is it really background knowledge to suppose that Joe will do his part in acting on the salient solution? It seems perfectly reasonable to suppose that Joe will do his part. It would seem that if a certain course of action is salient, it seems obvious that the other person would choose that option given that each person has a common end, and recognition of a common (salient) means to that end. The common means in this situation is recognition of the salient solution; the common end is that both Sally and Joe want to get out of this dilemma. So given that each has a common end, and each has available to them a common means to this end, this is good reason for acting in unison; it is also good reason to believe the other will do their part. We might be inclined to think that we cannot know for certain that the other person will do their part, but it would seem more reasonable to think that each other will do their part than not do their part. After all, it is not as though Sally or Joe could maximize his or her individual expected utility in any way other than to co-ordinate their efforts. Thus each will do their part if they are rational.

So it would seem that what is at issue here is not whether salience provides one with a reason to act, but whether we are justified in believing that the other will do their part in choosing to act on the salient solution. If we make an explicit argument for this position, we may see that each person is indeed rational to believe that the other will play his or her part in acting on the salient course of action.

It seems to me that people ought (in a pragmatic, not a moral sense) to do their part in a no-communication co-ordination problem if doing their part means maximizing individual expected utility. Let us consider the following argument:

1) To act on the salient solution is to maximize individual expected utility. (In this example, if both Sally and Joe choose red, both will escape with their lives. To escape with one’s life is to maximize individual expected utility in this case)

2) To act in a way that does not maximize one’s individual expected utility, is, by definition, to act irrationally.

3) It has been stipulated that Sally knows that Joe is rational, and Joe knows that Sally is rational

4) Hence, it follows that each will know that the other will act on the salient, because to act on the salient is to maximize one’s individual expected utility, and this is what rational people do.

5) Therefore, Sally and Joe will both be well justified in the belief that the other will act on the salient solution.

So then, exactly what role does salience play in the rational decision-making process? Does salience provide a reason to act? I agree with Gilbert that salience alone does not provide a reason for action, but I do not agree that an agent has no reason to believe the other player will do her part in choosing the salient solution. I would argue that salience, where identifiable, does provide a means by which agents may co-ordinate their actions; it is the first step in a line of reasoning for choosing a course of action. However, we cannot rely completely and solely on salience to motivate action. We also need to have good reason to suppose that the other agent will do his or her part in the situation. As we have seen, when two agents are rational, and this fact about each other is out in the open, then each agent is well justified in her belief that the other will do her part in choosing the salient. So it would seem that in all situations where each agent knows that the other agent is rational and is trying to maximize her individual expected utility, and a salient solution has been identified, salience will play a part in how each will act, but it will not provide a reason to act.

Bibliography

Margaret Gilbert, “Rationality and Salience,” Philosophical Studies 57 (1989), 61-77.

Richmond Campbell, “Background for the Uninitiated,” in Campbell and Sowden, eds., Paradoxes of Rationality and Co-operation: Prisoner’s Dilemma and Newcomb’s Problem, (The University of British Columbia Press: Vancouver, 1985)

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