V. Group Agency
The Metaphysics of Agency
If we change our perspective from that of individual decision making to one of collective choice, the free rider problem seems to take on a different dimension. From a social perspective, it is clearly better for everyone if no one free rides than if all do. This remark merely restates the problem. But if we go on to suggest that a justification for not free riding remain at the social level and deny the need to reinforce this justification with reasons that individuals can understand and find persuasive, then we are going beyond a mere reformulation of the conditions that constitute our problem. We are challenging the primacy of individual decision makers as the agents to address when justifying and rationalizing action.
One way to depart from an individual-based justification would be to take seriously the metaphysical reality of group minds or agency. Another route, which is a less drastic challenge to individualistic justification, advocates collective principles of choice: each individual decides what to do as if she were deciding for the group. I will defend the primacy of the individual and individual-based principles of choice by arguing against solutions based on social agency. Neither group minds, group agency, nor rules of choice that focus on the consequences of collective decisions, will emerge as promising approaches.
When one head is better than two
Imagine this story. The District Attorney has the driver and the safe cracker in a bank robbery arrested on minor charges. He is too busy to see the suspects in person, so he sends the driver and safe cracker a letter explaining the situation. The deal he offers presents a standard prisoner's dilemma. If one confesses and the other doesn't the one who confesses goes free, while the other gets 10 years. If neither confesses, both can expect one year in jail, while if both confess, both can expect three years.
Unknown to the District Attorney, the driver and the safe cracker are the same person. What does the driver do? Obviously, he refuses to confess. So does the safe cracker. Suppose the driver must make his decision on Monday and the safe cracker on Tuesday. Why on both days does he choose to keep mum? The answer cannot be that the driver is able to "communicate" with the safe cracker and forge an "agreement". When there are two criminals, as in the standard prisoner's dilemma, communication and the opportunity to reach an agreement does not induce cooperation, as long as the agreement is not binding or enforceable. Each prisoner has an incentive to break his agreement, even if open communication allows him to make one. If communication and agreement does not lead to cooperation in the two-person Prisoner's Dilemma, it cannot be what explains success in the one-person "Prisoner's Dilemma". In so far as we can sensibly speak of an agreement where there is only one person (or "making an agreement with oneself"), an "agreement" is no more binding in the situation of one prisoner than it is in the situation of two prisoners. People often break their promises, including those they pretend to make with themselves.
Further, we might eliminate "communication" even when there is only one prisoner. Before making his decision on Tuesday, the robber will be forced to take a pill that causes him to forget what decision he made on Monday. Should he confess on Tuesday? Only if he confessed on Monday. The game is simply one of coordination. If he makes the same choice on Monday and Tuesday, he gets one or three years, depending on the choice, while if he makes divergent choices, he serves 10 years, guaranteed. Since not confessing both days is better than confessing both days, the lone prisoner decides never to confess, even if the self deciding on Tuesday has no way of "communicating" with the self deciding on Monday.
With a single bank robber, the justification for never confessing is very straightforward: it's better for the agent. A single agent considers what to do over the course of a couple of days and performs that action she thinks would have the best expected outcome. In a one-person "Prisoner's Dilemma", the best expected outcome is for the prisoner to never confess. (The one-person game is not really a traditional Prisoner's Dilemma. Most authors would define the latter as necessarily a two-person game, but the matrices look the same.)
The above dilemma offered a prisoner an opportunity to confess, but it could just as well have offered a contributor an opportunity to "free ride". Suppose there are two isolated opportunities to contribute $10 or nothing to a common kitty. The kitty is then divided up equally among the players, with a 49% bonus to each. For example, if the player with the first opportunity to contribute gives $10 and the player with the second opportunity gives nothing, each will receive $9.90 ($5 + $4.90).
If two purely self-interested people play this game, without binding agreements, neither will contribute. Each reasons that he must divide his $10 contribution with the other person and receive only $4.90 in compensation. Obviously, both not contributing is worse for each than both contributing.
What if a single person plays this contribution game, having an opportunity to contribute to the kitty during two consecutive periods? Obviously, he contributes during both periods, same as in the one-person "Prisoner's Dilemma" situation. So the one-person "Prisoner's Dilemma" is quite relevant to the problem of the voluntary provision of a public good.
Suppose that neuroscience has advanced to the point where a complete functional map of the brain is well known. A scientist can create a mind by setting up the appropriate functional connections using whatever hardware he prefers. Instead of having electrical and magnetic signals stand in for neurons, he decides to employ a very large number of people, the population of China, perhaps. This collection of people passes the Turing Test, seems to have beliefs and desires distinct from those of any member of the population, and receives the American Cognitive Scientist's award for most plausible artificial person of the year. Call her "Shelly".
Put Shelly in the one-person "Prisoner's Dilemma" situation and what does she do? She refuses to confess on both days, of course. Put her in the contribution game situation and what does she do? She contributes on both occasions, of course. Shelly is not just many people acting in concert; she is a group mind. The justification Shelly has for never confessing or twice contributing is exactly the same as before. The safe cracker and the driver, being literally of one mind, wants what's best for himself; he wants to spend less time behind bars and more time free to research bank floor plans. The potential contributor wants to walk away with the most money she can. So does Shelly. Justifying a contribution is easy because it leaves Shelly better off.
We will have to answer a few more questions to satisfy the skeptics. Why does each person perform the action she is assigned to perform by Shelly's creator? Perhaps each is paid to do her job professionally. If so, then the skeptic will say that the justification Shelly has for contributing only masks the more basic justification each human component has for doing her task. But this need not be so. Suppose each person is hypnotised to do her elementary task, or takes a drug that controls her behavior. She doesn't have a justification for doing what she does, she just does it. This does not prevent Shelly from having a good reason for her twice contributing to the kitty. Shelly has as much a justification as the safe cracker has for not confessing. The safe cracker's neurons don't have a justification for firing. Further justification is not required. Shelly has good reasons for contributing on both occasions in the contribution game. Our task is completed once we have articulated what those conclusive reasons are. Once we have explained why Shelly ought to contribute, how she is justified in doing so, our job is over. Our project is not to explain physiologically how Shelly manages to contribute twice. It is simply to justify Shelly's contribution. This is easy: Shelly does better if she contributes.
Shelly is not only an artificial person, but a fictional one. As it happens, no such mind, or equivalent substitute, actually exists. While in principle one might be able to justify voluntary provision using the notion of a group mind, in reality, no present collection of individuals interact in the intricate and complex ways required by a functionalist definition of mental states. The structure of organizations or social institutions such as corporations or governments does not come close to possessing the functional properties of a mind. So Shelly is not a model on which real people can rely to rationalize their voluntary contributions.
A second argument for social agency
Instead of looking for group minds, functionally defined, one might look for group agents, defined by other means. One might argue for the reality of group agency not by pointing out functional relationships, but by suggesting that group or social agency is presupposed by much of our talk and thinking about collective action. Not only do we ascribe intentional states such as belief, preference and choice to groups, but we evaluate, criticize and prescribe group behavior by the same standards we apply to individuals.
For example, Isaac Levi writes that
"...anyone prepared to attribute beliefs, values and choices to groups as well as to individual humans and to think that such values, beliefs and choices ought to be regulatable by the same principles of rationality as are applicable to human agents recognizes such social entities as agents in the only sense that matters here..."
We might put the argument as follows:
(i) Only agents have propositional attitudes, such as beliefs, or are the subject of normative evaluations.
(ii) Groups have propositional attitudes, such as beliefs, and are subject to normative evaluation.
(iii) Therefore, groups are (social) agents.
While this argument purports to prove that groups are agents, note that it does not prove that the agency involved is equivalent to a group mind. Quite possibly, the conditions for something to be a mind are more demanding or different than the conditions for something to be an agent. Perhaps minds have sensations (such as feeling hot or cold) and agents do not. I am not sure whether we ought to think of minds as different from agents. But suppose we do. Suppose the criteria for having a mind are different than the criteria for being an agent. Indeed, it is not difficult to imagine some dreamers who are no more than isolated, inactive thinking organs and some movers and shakers that have no sensations or emotions. We might call the former, "inert minds", and the latter "mindless agents".
Let's return to the syllogism above. Justification, as I conceive of it here, is a matter of providing reasons for an action, either prospectively to recommend that an action be performed, or retrospectively, to ascribe praise or blame for an action that was already performed. If there is an agent, then prescribing a future action or criticizing a past action is appropriate. Hence, if the above argument were to establish its conclusion, then this would allow for another dramatically different way of thinking about cooperation and collective action. One would be able to present unique ways of justifying the voluntary provision of public goods, quite unlike others we have considered in prior chapters or will consider in later ones.
Does the argument establish its conclusion? I think it does not. Both premises ought to be rejected. Consider the first. We sometimes ascribe propositional attitudes to entities that we do not consider to be bona fide agents, in the sense of purposeful, rational sources of action. We speak about genes being selfish and thermostats knowing when to turn off a furnace. We say that "heat seeking missiles like hot truck engines" and "atoms want to fill their shells with the right number of electrons".
Such talk and thinking is merely metaphorical. The ascription of beliefs and desires to non-living things does not imply that they are agents in the full sense of that term. Genes, thermostats, missiles and atoms are not agents. The same is true of normative talk. "A cardinal ought to throw parasitic cowbird eggs out of its nests", but unfortunately for the reproductive success of the species, "a cardinal will foolishly let the cowbird egg hatch and eventually crowd out its own young". This does not imply that cardinals are agents in the sense of a thing that deliberates and can justify her actions.
Defenders of teleological explanations may not accept my characterization of the above sort of talk as "merely metaphorical". Some defenders of teleological explanations consider them perfectly legitimate when (but only when) other forms of explanation are lacking. However, in many instances other forms of explanation are not lacking (as with regard to atoms, missiles and thermostats). Nor are they lacking in the instances that particularly concern us here, namely, group behavior. Sociological or anthropological explanations that conform to the strictures of methodological individualism attempt to explain human behavior purely on the basis of individual beliefs and desires. Assuming that the strictures of methodological individualism can be met, this defense of teleological explanations need not detain us further.
Other defenders of teleological explanations argue that such explanations are perfectly compatible with laws that causally explain human behavior without appealing to a thing's purpose or direction. Taking the "intentional stance" towards a thing enhances the predictive power of the person who takes such a stance, even when other forms of explanation are also available (in principle or in actuality), especially when the other forms of explanation are less accessible, more cumbersome or more computationally demanding.
Here, however, we are not concerned with predictive power. We are concerned with rational and moral justification. The concept of justification only applies to agents that deliberate, choose and can defend their choice with reasons. We often talk as if we were attributing beliefs and desires to things that we know do not deliberate. So even if teleological explanations which attribute beliefs and desires to non-human things are legitimate, they do not provide grounds for believing that these things deliberate or can justify their actions. My point is limited to denying that such talk (or the attribution of propositional attitudes) is good evidence for a strong form of agency, an agency capable of deliberation and to whom it makes sense to address questions of justification.
The point that normative talk does not necessarily imply agency in the relevant sense is reinforced by a close examination of the second premise. We shall see that there can be normative evaluations of group actions without supposing that these evaluations serve as guidance or criticism. We can evaluate an action without hypostasizing an agency behind it, at least not an agency to whom guidance or criticism is appropriately addressed.
So now consider the second premise, in particular, the claim that groups are the subject of normative evaluations. How we respond to it depends on what we are going to call a group. A group might be any arbitrary collection of individuals that interests us or it might be some more cohesive set of people interacting in certain significant ways. Consider first arbitrary sets of individuals.
It might seem that we can and do normatively evaluate the actions of arbitrary groups, or at least that such evaluations are not bizarre.
Suppose, for example, that it would be safest if everyone were to drive under 55 miles per hour, but that it is more dangerous for one person to drive under 55 mph if everyone else is driving at 95 mph. Assume that everyone in fact is driving at 95 mph. Then it would not be the case that any one person ought to drive under 55 mph, but it would be the case that everyone ought to drive under 55 mph. There are a host of evaluations similar to this that we could and possibly do make of groups. These evaluations are not reducible to evaluations we make of the individuals in the group.
If we are tempted to make these evaluations, then we must be clear that they do not amount to evaluations of subjective rightness, but only of objective rightness. The distinction between objective rightness and subjective rightness is closely related to the issue of agency. Evaluations of objective rightness do not presuppose an agent, while evaluations of subjective rightness do presuppose an agent; it presupposes precisely those sorts of agents for whom justification is a relevant issue.
When is an action objectively right and when is it subjectively right? There are different ways to draw the distinction. For our purposes we may say that an action is objectively right if and only if it leads, or would lead, to the best possible consequences. An action is subjectively right if and only if it is what the agent ought to do, given what she has reason to believe at the time. Evaluating group action according to objective rightness can often be relatively straightforward, especially if all of the alternatives are better or worse according to a simple and appropriate criterion (as the Pareto standard will be in some instances). What everyone does either is or is not the best that they could do.
What would it mean to evaluate a group's action according to the standard of subjective rightness? It would require a notion of the group as an entity with a distinct set of beliefs. The evaluation of what is subjectively right would have to be relative to what the group had reason to believe. If a group is going to have beliefs, it seems unlikely that the group could be any arbitrary set of individuals. Instead, they must be related in some significant way and capable of communicating. However, the sort of evaluation we make when we say that everyone ought to drive under 55 mph is an evaluation about an arbitrary set of individuals. The group of people, all of whom ought to drive under 55 mph, could be any collection of people who happen to be driving along the highway. In fact, it could include people driving along many different and disparate highways, say, one in the U.S. and one in Australia.
Our willingness to evaluate the objective rightness of actions performed by arbitrary groups does not imply that we regard these groups as agents. Making evaluations of objective rightness has little bearing on what we are willing to prescribe or criticize. So here again we have reason to reject the first premise of our earlier argument for social agency.
The best that we can say in favor of making evaluations of objective rightness, in general, is that they are easy evaluations to perform and that they might serve as first approximations for evaluations of subjective rightness. However, in situations in which what is best for the individual to do is not the same as what is best for everyone in a group to do, all of the important work is going to take place in getting past the first approximations.
Consider again the highway example. Since there is no group agent that possesses beliefs, the group cannot be the subject of evaluations of subjective rightness. So evaluations of subjective rightness must apply to individuals in the group. Unfortunately, there is no simple relationship between the objective rightness of a group's action and the subjective rightness of an individual's action who is a member of the group. It is objectively right for everyone to drive under 55 mph. But if I believe everyone else is driving over 95 mph, then it is subjectively wrong for me to drive under 55 mph. What is subjectively right and wrong for a person to do depends crucially on what that person has reason to believe.
Suppose everyone is driving under 55 mph. Then it is objectively right for the group to drive under 55 mph and it is objectively right for each person in the group to drive under 55 mph. One might even be tempted to propose a general principle stating that if a group act is objectively right, and it is performed, then each individual constituent act is objectively right. This principle, while true, is not helpful. For while the principle tells us how, in some situations, to get from objective rightness for group actions to objective rightness for individual actions, it does not tell us how to get from there to subjective rightness. An individual's action may be objectively right, the group's action, of which the individual's action is a constituent, may be objectively right, and still the individual's action is subjectively wrong. Suppose, for example, that while everyone is driving under 55 mph, each person has good reason to believe that everyone else is driving over 95. Then each person is subjectively wrong to drive under 55 mph.
We may make an evaluation of any action, whether it be of an agent or not, in terms of objective rightness. Is it objectively right that the bear maul the park ranger or not? Would it be objectively wrong for the sun to explode? We are as free to ask these questions, as we are to ask about the objective rightness or wrongness of group actions. Such questions simply invite consideration of the goodness of an action's effect. This is fine. We are not entitled, however, to evaluate bears or stars for the subjective rightness of their actions. Subjective rightness only applies to agents capable of deliberation.
As I have said, justification is a matter of providing reasons for an action, either prospectively to recommend that an action be performed, or retrospectively, to ascribe praise or blame for an action that was already performed. Objective rightness is not directly relevant to the task of justification. If a person believes that everyone else is driving over 95 mph, then she should not drive under 55 mph. Driving under 55 mph is not justified, although it may be objectively right, both for the individual and for the group of which the individual is a member.
Similarly for situations involving public goods. It may be objectively right for a group of people to support a public good. If everyone does support the good, it may even be objectively right for each person to support that good. However, from this one cannot conclude that each person is justified in supporting the public good. If each person has reason to believe (mistakenly) that everyone else is not supporting the good and that it would be wasteful to support the good alone, then supporting the good is subjectively wrong and unjustified. Showing that an action is objectively right is no justification for performing the action.
Let us briefly review our progress. If one could view groups as agents in their own right, then one could provide a justification for voluntary provision. Further justification at the individual level would not be required. I have considered a possible argument for regarding groups as agents. It rests on two premises. I offered reasons to reject the first premise and promised that further reasons would also follow from our consideration of the second premise. I suggested that our response to the second premise depended on our interpretation of the concept of a group. I argued that if we think of a group as any arbitrary collection of individuals, then our normative evaluations will not imply the relevant sense of agency. Such evaluations have no bearing on the issue of justification.
What about non-arbitrary groups? Might we attribute beliefs to them or make normative evaluations which would justify our considering as agents these kinds of groups?
In making the above argument, I have assumed that arbitrary groups, such as the collection of people driving on Highway 66 in the U.S. and M4 in England, do not have genuine beliefs. If they do not have beliefs, we cannot talk about what is subjectively right for the groups to do. However, if we consider less arbitrarily composed groups, and show that these groups have beliefs, then we might be able to talk about what is subjectively right for the group to do and hence provide a justification for the group to perform a particular action.
To take seriously the notion of group agency one would have to do two things. One would need to show that non-arbitrary groups have beliefs and one would need to explain what a non-arbitrary group is.
One might attribute well defined beliefs to a cohesive group, say a reading discussion group, without provoking serious misunderstanding. One might say, or think, for example, that the Monday Night Reading Group believes that Philip Larkin's "Church Going" is a moving poem. There might even be conventions or explicit rules which determine the group's beliefs, given certain other facts, such as what each person in the group believes. These conventions or rules may be more complex than a simple unanimity principle (if everyone in a group believes some proposition then the group believes that proposition). Unfortunately for our purposes, the sorts of groups to which one might plausibly attribute beliefs are not the sorts of groups that most concern us. The supporters of a particular public good are not like the members of a reading group. Our kind of groups do not have beliefs. We can see this more clearly if we consider exactly what sorts of groups are cohesive enough to have beliefs.
Consider the following attempt to capture the notion of belonging to a cohesive (non-arbitrary) group. Someone belongs to a cohesive group if and only if:
(i) she expresses her willingness to be a member of the group
(ii) she intends (i) to be common knowledge among members of the group
(iii) (i) is common knowledge among members of the group.
Not only does this definition exclude groups with involuntary members, such as members of families and citizens of countries, but more importantly for our purposes, it excludes large scale groups, especially of people who cannot readily communicate with each other, such as public radio listeners.
The second sort of group is excluded because it does not seem possible to have common knowledge about a person's self avowals without communication. I cannot know that Mary has expressed her willingness to be a member of a group if I have no knowledge of Mary's actions or I don't even know that Mary exists.
One might suggest that I have knowledge of Mary's action under the right description. Members of a group have common knowledge by description, not by acquaintance. For example, members of the ACLU may have each expressed their willingness to be members of that group. Each knows that others who have paid their dues have expressed their willingness to be members of the group. Others know that each person knows this, and so on. Indeed, if one supposes speakers have common knowledge of the conventions of a language, then one must suppose some such knowledge by description.
I have two objections to this defense. First, introducing knowledge by description would seem to prove too much. I know that anyone who has read this dissertation has read this dissertation. Suppose a stranger to me, John Smith, reads this dissertation. Do I thereby know that John Smith had read this dissertation? Hardly.
Second, what work is done by the two conditions involving common knowledge? In the example I've given above, the description itself seem to be all we need to determine group membership. Members of the ACLU are those that have paid their dues, those that have expressed their willingness to be members of the ACLU. The requirement of common knowledge seems superfluous. It does not seem superfluous in the small group case, however. The requirement of common knowledge removes certain instances in which there is expressed willingness and not group membership. Jack and Jill want to ride the train together, each expresses his/her willingness to others, but not to each other. Each may even know that the other has expressed his/her willingness, yet if each thinks the other is ignorant of his/her own expression of willingness, they do not form a group that rides the train together. The reason is that they do not have common knowledge.
The trouble is that they do have common knowledge by description. Jill has expressed a willingness to ride the train with Jack. Jack knows that anyone who has expressed a willingness to ride with him has expressed a willingness to ride with him. So in the same sense in which the members of the ACLU know that other members have expressed their willingness to join the ACLU, Jack knows that Jill has expressed her willingness to ride the train with him. Jill knows that anyone who knows that she has expressed her willingness to ride the train with Jack, knows that she has expressed her willingness to ride the train with Jack. Hence, in the same sense as with the ACLU example, Jill knows that Jack knows that she has expressed her willingness to ride the train with him. They each have common knowledge by description.
I suggest that either common knowledge does not apply in the instance in which there is no communication, or else it does apply, and thus allows Jack and Jill to be members of a cohesive group, which seems implausible.
To sum up the present discussion, arbitrary groups, which might include contributors to a public good, do not have beliefs, while cohesive groups, which perhaps do have beliefs, are not the only, or even the primary, groups that contribute to large scale public goods. Hence, no convincing argument has been offered to suggest that the large scale groups, such as the set of people who contribute to a particular public good, are the kind of groups that have beliefs or engage in collective deliberation. We are left without a reason to believe in the reality of social agents useful for our purposes.
Before leaving the metaphysics of agency, I wish to add one last point about competing levels of justification. Imagine asking a contributor to a public good why she did not free ride. She responds, "I know that I am better off if I do not contribute, but as a group, we are better off if we contribute. That is why we contribute: it is best for us." Since she knows that her contribution benefits others at some cost to herself, I suggest that it is possible to interpret this person's words and action as strong evidence that she in fact cares positively about the welfare of others in her group (she is altruistic). Since we must suppose individual deliberating agents anyway to explain other kinds of actions, this interpretation provides the simplest rational justification of her behavior, without introducing additional metaphysical entities.
Collective Principles of Choice
Let us now examine an argument in favor of voluntary provision based on collective principles of choice. Collective principles of choice consider the effect not of the individual's action, but of everyone in a group performing their role in a group action. So, for example, a collective principle of choice might recommend that if you are a member of a certain group and if the group acting in such and such a fashion, which includes your doing such and such, produces the best consequences, then you ought to do such and such. In other words: if you are a member of a group and if there is an assignment of actions to individuals which, if performed, would produce the best possible consequences, then you ought to perform the action specified in that assignment.
Each person is capable of acting in accordance with the above principle. The justification of this principle would not involve an appeal to the notion of group agency. Instead, we might justify this principle on the grounds that if everyone followed it, people would probably produce more good than if they followed any other principle. Perhaps the principle is particularly helpful in allowing people to act effectively in situations where principles that consider only the consequences of individual action would lead to dramatically worse results. The prisoner's dilemma would be one such example. Following the collective principle leads to mutual cooperation, while following the individual principle leads to mutual defection.
However, there are also many examples in which having some, but not all, relevant participants following the collective principle leads to disaster. If everyone under a repressive dictatorship were to ignore what the dictator said and pretend that he was a madman who merely imagines himself to be a dictator, then this might be best for all concerned. However, if a few people in the right places and positions were not willing to go along with this conceit, then the whole plan would crumble as soon as the dictator starts executing the first insubordinates who disobey his orders. Many people might die needlessly before others finally recognized the folly of following the collective principle.
One might modify the collective choice principle so that consideration is given to who is and who is not prepared to join in a group action. But if this approach is made sufficiently sensitive to one's expectations concerning everyone else's action, it no longer seems distinguishable from the individualistic principle, which can be stated much more simply.
Might there be instances in which the collective principle, modified to accommodate non-cooperation, still diverges from the individual principle and in which our intuition about what action is rational agrees with the collective principle? I think not, but consider the following example.
Suppose a group of voters share a desire for electoral reform. If at least 90% of them go to the polls then they will achieve their goal. If less than 90% vote, however, corrupt officials will be able to rig the election to give the appearance of popular support for the status quo. So the second best outcome is for less than 10% of the population to vote.
If one followed the collective principle, one would definitely vote if one believed everyone were prepared to cooperate. Suppose everyone is prepared to cooperate. Then each performs their share in the group action that has the best consequence. In this instance, each ought to vote.
What about the individual principle? This depends on what each person thinks everyone else will do. Suppose that each person begins with a prior probability of 75% that any particular person will vote. The chances that more than 90% of the total population will vote will be extremely small. Thus each person will decide that voting would be a mistake. A more sophisticated procedure would allow for dynamic adjustments to take account of mutual assessments of the likelihood that others will vote. I would adjust my estimation of others voting, given their estimation of my estimation of their voting, etc. This would only further reinforces the choice of not voting.
This reasoning seems to suggest that the two principles diverge. We should not be so easily deceived. We have made an assumption in considering the collective principle of which we have not taken advantage in considering the individual principle. We have assumed that everyone is prepared to cooperate. Why not let each person assume that everyone else will vote (say, because she thinks everyone else is going to follow the collective principle) and see where she ends up after recursive Bayesian reasoning? Obviously, she will then decide to vote. If each person believes that everyone else is going to act on the collective principle, then the individual principle tells each person to vote.
On the other hand, if we do not assume that each person believes that most everyone else will follow the collective principle, then neither principle necessarily advocates voting. The collective principle recommends voting if the group's doing so would be best, given the number of people one can expect to belong to the group. But unless one expects enough others to follow the collective principle, one cannot be sure that enough people will belong to one's group to make voting worthwhile. Similarly, the individual principle recommends voting only if one expects enough others to be disposed to vote. Believing that others are following the collective principle is not the only reason one might have for confident optimism about what others will do. A history of similar behavior or salience would breed comparable results.
The advocate of the collective principle cannot have it both ways. She cannot refine the principle so that it doesn't mislead people when cooperation from others might be lacking and at the same time have a principle that is distinct from an individual principle in which each person decides what would be best to do individually, given what she believes others will do.
So far we have discussed a situation that resembles an Assurance Game. There were essentially two equilibrium points: everyone votes or everyone does not vote, with one point (where everyone votes) clearly having a better outcome than the other. Now suppose that there is only one Nash equilibrium point and the outcome for each person at this point is the best possible. (Recall that a set of strategies is in Nash equilibrium if no one person could improve her payoff by choosing a different strategy, given the strategies of everyone else.) Might people following the individual principle of choice be unable to coordinate their actions so as to achieve the benefits of this point, while people following the collective principle have no such obstacle? Consider the following game.
A person, reasoning under the individual principle, would want to avoid the penalty of -50 that she might receive were she to choose A or B. If she chooses C she is guaranteed an outcome of at least 3. Following a maximin strategy, for example, would lead one to choose C. On the other hand, a person reasoning under the collective principle, convinced that the other person was prepared to cooperate, would choose A, since each receives her best outcome if the pair chooses A.
Here again, we should only conclude that the principles diverge if we make different assumptions about the followers of each principle. The followers of the individual principle will choose C only if they have doubts about the rationality or preferences of the other player, the existence of common knowledge about these facts and the rules of the game, or if there is an opportunity for a mistake in the execution of a decision (a "trembling hand").
Suppose each player thinks the most rational strategy for each to play is C. Then the column player would know that the row player is going to choose C. She would then not play C, but A, which has the slightly higher payoff of 4. The column player ought to know this, which in turn leads her to play A herself. So both end up playing A after all. We would have arrived at the same result had we started by considering the row player's best strategy if the column player chooses C.
Maybe the player acting on the individual principle believes either A or C would be rational. Still, she will prefer A, which strictly dominates C once B has been eliminated. There is no reason why a rational player under the assumption of common knowledge would think that the other player might play B.
Rational players with common knowledge will never reject a unique Nash equilibrium point in a game with well defined
payoffs and choices, where "well defined" excludes certain troublesome infinite sets.
I conclude that we cannot find an adequate justification for the voluntary provision of public goods either by considering the metaphysics of agency or by recourse to group based principles of choice.
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