Testing Axioms Against Human Reward Divisions in Cooperative Games

Axiomatic approaches are an appealing method for designing fair algorithms, as they provide formal structure for reasoning about and rationalizing individual decisions. However, to make these algorithms useful in practice, their axioms must appropriately capture social norms. We explore this tension between fairness axioms and socially acceptable decisions in the context of cooperative game theory. We use two crowdsourced experiments to study people's impartial reward divisions in cooperative games, focusing on games that systematically vary the values of the single-player coalitions. Our results show that people select rewards that are remarkably consistent, but place much more emphasis on the single-player coalitions than the Shapley value does. Further, their reward divisions violate both the null player and additivity axioms, but support weaker axioms. We argue for a more general methodology of testing axioms against experimental data, retaining some of the conceptual simplicity of the axiomatic approach while still using people's opinions to drive the design of fair algorithms.