Dividing a cake for the irrationally entitled

TL;DR

This paper investigates cake-cutting protocols where agents have irrational entitlements, proving that such scenarios require arbitrarily many queries to ensure fair division respecting all entitlements.

Contribution

It introduces a formal model for cake division with irrational entitlements and proves the necessity of infinitely many queries in certain cases.

Findings

Irrational entitlements can force protocols to require infinitely many queries.

The model formalizes the interaction between mediator and agents in cake division.

Ensures fair division respecting complex entitlement structures.

Abstract

A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the agents, but can query the agents to make cuts and appraise slices in order to learn. We prove that if one of the entitlements is irrational, then the mediator must use a protocol that involves an arbitrarily large number of queries in order to construct an allocation that respects the entitlements regardless of preferences.