Morality is Fractal

Abstract

If the basic purpose of moral norms is to coordinate on the conditions under which one should cooperate in social dilemmas, this paper shows that the boundaries of such conditions must be fractal. In other words, as one focuses on the border of the area in signal space where the best response flips from cooperate to defect, the adversarial nature of a social dilemma means there must always be some possible detail, otherwise irrelevant, that can flip the best decision, and some point can always be found that will be undecidable at any fixed resolution. Thus any finite-length moral code, as an approximation to that infinitely detailed boundary, faces a tradeoff between leaving gains from cooperation on the table, and vulnerability to exploitation. Implications are discussed as to the intrinsically dynamic nature of norms and institutions, the impossibility of identifying law with morality, and runaway cultural selection.

JEL Classification: C65, C73, D02, K12