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Dividing a cake for the irrationally entitled

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  • Florian Brandl
  • Andrew Mackenzie

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.

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  • Florian Brandl & Andrew Mackenzie, 2025. "Dividing a cake for the irrationally entitled," Papers 2508.09004, arXiv.org.
    • Handle: RePEc:arx:papers:2508.09004
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    References listed on IDEAS

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    1. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    2. Rustamdjan Hakimov & Madhav Raghavan, 2023. "Improving Transparency and Verifiability in School Admissions: Theory and Experiment," Rationality and Competition Discussion Paper Series 376, CRC TRR 190 Rationality and Competition.
    3. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 341-378, September.
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