Throw One's Cake --- and Have It Too

TL;DR

This paper explores how discarding parts of a heterogeneous cake can lead to more socially optimal fair divisions among players with different tastes, challenging traditional fairness constraints.

Contribution

It introduces the concept that discarding some cake can improve social welfare in fair division, providing tight bounds on this improvement.

Findings

Discarding cake can increase social welfare in fair division.

Asymptotic bounds on social improvement are established.

Fair division of a subset can outperform dividing the entire cake.

Abstract

We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such discarding.