In the last post we considered a model of the evolution of justice according to evolutionary game theory. We saw that according to such (overly) idealized models, the emergence of social equality is relatively likely in accordance with a comparatively a-rational process. In this post we will consider the evolution of commitment, especially the commitment to follow through with threats that are not in one’s best interest to follow through with.
Last time we considered the scenario in which we are to divide a cake into two portions behind a veil of ignorance as to which portion we would receive ourselves. This time the scenario is one in which we divide the cake into two portions knowing which one is for you and which is for the “other guy.” The only catch is that the person has to approve of the divide or no deal; a “take it or leave it” scenario.
The idea is that a person can threaten to reject a proposal if a deal is unfair enough, but when such an instance arises it really isn’t in the agent’s interest to follow through with his threat. The point is that people actually do follow through with their threat in real-life scenarios, and this seems to cry out for an explanation.
“A strategy that includes a threat that would not be in the agent’s interest to carry out were she called upon to do so, and which she would have the option of not carrying out, is a defective strategy. This point is not really confined to threats. In a credible contingency plan for a situation in which an agent faces a sequence of choices, her plan should specify a rational choice at each choice point, relative to her situation at that choice point. Such a contingency plan exhibits modular rationality in that it is made up of modules that specify rational choices for the constituent decisions.” (24)
Skyrms point is that the not uncommon sacrifice of personal benefits in order to punish the unjust or uncooperative demonstrates a significant lack of modular rationality. Not only that, but it doesn’t take a genius to see this in practice; indeed, it takes more intelligence to attempt a rational justification for such a strategy.
It should also be noted that this situation is qualitatively different from that of justice as fairness. The idea of justice may encourage people to not seek exploitative, and therefore likely to be rejected, offers. It may also serve to help in the identification of exploitation by those who will either take or leave the offer. But neither of these issues is really the point. The issue which is at hand is the seeming irrationality of a person’s being willing to sacrifice his own interests in order to punish potential exploiters by keeping commitments which were initially made as a deterrent.
Skyrms sets up a scenario in which eight strategies are interacting with each other, each consisting of three binary parts: demand 5 or 9 out of ten portions of cake, take or leave demands of 5/5, and take or leave demands of 9/1. Each of the eight strategies thus includes what to do when playing the part of the divider and the potential accepter/rejecter. When a population of evenly distributed strategies randomly interacts with each other the following set of strategies emerges as dominant:
Gamesman: demand 9, accept 1 and accept 5
Mad Dog: demand 9, accept 1 and reject 5
Under such circumstances, the gamesman takes over the majority of the population, but about 13 percent of the population remains mad dogs once all other strategies are eliminated since at that point there are no more demands of 5 to reject. The point worth noting is that a strategy of modular irrationality survives within the population in the form of the mad dog, though this is not really the form of it with which we are most familiar.
If the population begins with a slightly different concentration of strategies, the following set emerges:
Easy Rider: demand 5, accept 1 and accept 5
Fairman: demand 5, reject 1 and accept 5
If the population begins with 30 percent fairmen, with all other strategies being equal to each other, fairmen come to represent 64 percent of the population with the remainder being easy riders. In this case, modular irrationality actually comes to be represented in the majority of the population, it being a scenario far more in sync with what we are familiar with.
What is of interest is that all initial starting points lead to a polymorphism in which a modular irrational strategy always remains. Furthermore, “if you allow more possible demands, you typically end up with a more complicated polymorphism that contains several weakly dominated, modular-irrational strategies. As we increase the options, the evolutionary dynamics generates a richer set of anomalies.” (33)
An interesting scenario in which these results may shed some light is in tit-for-tat situations. Non-cooperators, in the take it or leave it game, will tend to be punished for their non-cooperation. However, punishment itself is non-cooperation and thus would itself merit punishment in the tit-for-tat situation of modular irrationality. It would seem that, given the situation, only modular rationality could ever break the cycle to retribution and reestablish cooperation.
This model, it would seem, does not provide a full explanation of how fairmen and easy riders could have originally emerged as a majority. Instead, it is meant more as an account of how this combination of strategies could have survived given the initial conditions which we specified.
Skyrms suggests that a possible explanation for the initial concentration of fairmen would be due to a generalization from principles of justice. This, to me, is not an implausible suggestion, especially when one considers that we are here speaking not of the propagation of agents who happen to have a particular strategies, but are instead talking about the propagation of the strategies themselves. Since imitation and learning are what counts here, invoking notions of generalization do not seem too inappropriate.
