Two wrongs don't make a right: The initial viability of different assessment rules in the evolution of indirect reciprocity

Indirect reciprocity models are meant to correspond to simple moral systems, in which individuals assess the interactions of third parties in order to condition their cooperative behavior. Despite the staggering number of possible assessment rules in even the simplest of these models, previous research suggests that only a handful are evolutionarily stable against invasion by free riders. These successful assessment rules fall into two categories, one which positively judges miscreants when they refuse to help other miscreants, the other which does not. Previous research has not, however, demonstrated that all of these rules can invade an asocial population-a requirement for a complete theory of social evolution. Here, I present a general analytical model of indirect reciprocity and show that the class of assessment rules which positively judges a refusal to help scofflaws cannot invade a population of defectors, whereas the other class can. When rare, assessment rules which positively judge a refusal to help bad people produce a poor correlation between reputation and behavior. It is this correlation that generates the assortment crucial in sustaining cooperation through indirect reciprocity. Only assessment rules that require good deeds to achieve a good reputation guarantee a strong correlation between behavior and reputation.