Quasi-magical thinking and superrationality for Bayesian agents

As part of our objective and subjective rationality model, we want a focal agent to learn the probability that others will cooperate given that the focal agent cooperates () or defects (). In a previous post we saw how to derive point estimates for and (and learnt that they are the maximum likelihood estimates):

, and

where is the number of times Alice displayed behavior and saw Bob display behavior . In the above equations, a number like is interpreted by Alice as “the number of times I cooperated and Bob ‘responded’ with a defection”. I put ‘responded’ in quotations because Bob cannot actually condition his behavior on Alice’s action. Note that in this view, Alice is placing herself in a special position of actor, and observing Bob’s behavior in response to her actions; she is failing to put herself in Bob’s shoes. Instead, she can realize that Bob would be interested in doing the same sort of sampling, and interpret more neutrally as “number of times agent 1 cooperates and agent 2 defects”, in this case she will see that for Bob, the equivalent quantity is .