We use computer simulation to identify a process by which cooperation evolves without iteration, and evolves better in large than in small societies. It is based on an empirically supported heuristic for deciding whether to enter noniterated prisoner'r dilemma games, namely, Expect others to have the same dispositions as yourself. Players are assigned a probability of cooperating that also defines their expectations about others’ behavior and thus their willingness to play. The carrying capacity of the ecology is 10,000. Players multiply by 2 if their aggregate payoff in a given round (1) places them among the more successful 5,000 and (2) is more than zero. We find that the most adaptive disposition is toward the mean of the population. That is where individuals have the optimal mix of consummated plays with more cooperative players and unconsummated plays with less cooperative ones. When encounters occur by proximity, fortuitous clusters toward the cooperative tail will grow and dominate the society. Such clusters are more likely in large societies.
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