Fair cake-cutting for imitative agents

Abstract

We investigate cases of preference change in the context of cake-cutting problems. In some circumstances, believing that some other player can be credited with a particular preference structure triggers a preference shift by imitation. As a result of this, players may experience regret. However, in typical examples the extent of the change (and the ensuing regret) cannot be anticipated, so players cannot adjust their behavior beforehand. Our goal is to describe the phenomenon, provide a formal model for it, and explore circumstances and allocation procedures that may alleviate some of its negative consequences. In the face of utility shifts we propose a new criterion for fairness, which we dub Ratifiability; in a ratifiable allocation rational players are happy to stick to their choices, in spite of the changes in utilities they may experience. We argue that this embodies a sense of fairness that is not captured by other properties of fair allocation.