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This paper systematically evaluates 1,048,576 moral systems across all two-player social dilemmas to understand the conditions for cooperation via indirect reciprocity. It finds that all stable, cooperative systems require a discriminating strategy that aligns with a consistent norm, where actions are judged according to the strategy's prescribed behavior. Specifically, the "contrite discriminator" strategy, which cooperates to rectify past misdeeds, emerges as the sole stable strategy in the presence of small errors, unifying prior research on indirect reciprocity.
Cooperation universally hinges on moral systems that "practice what they preach," with the contrite discriminator emerging as the only robust strategy across all social dilemmas.
A leading explanation for why humans cooperate with strangers is indirect reciprocity: when conduct is observed, individuals earn good reputations by cooperating with the deserving. Previous research has identified many"moral systems"that sustain cooperation through indirect reciprocity - each pairing a strategy for how to act with a norm for how to judge others - yet what makes them succeed, and whether that success generalizes beyond the donation game, has remained unclear. Here we evaluate all 1,048,576 moral systems whose norms condition on both players'reputations and actions, across every two-player social dilemma. We find that every highly stable, cooperative system pairs a"discriminating"strategy - one that cooperates with the good and defects against the bad when in good standing - with a"consistent"norm that deems good exactly those who act as the strategy prescribes. Such systems"practice what they preach"and preach what they practice. In the limit of small errors, only one strategy paired with a consistent norm remains stable across all social dilemmas: the"contrite discriminator", which cooperates to make amends when its standing is bad. Our results unify decades of research on indirect reciprocity, revealing moral consistency as the common ingredient of every stable, cooperative moral system.