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arXiv · 2106.11178

Thou Shalt Covet The Average Of Thy Neighbors' Cakes

Jamie Tucker-Foltz
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Abstract

We prove an $Ω(n^2)$ lower bound on the query complexity of local proportionality in the Robertson-Webb cake-cutting model. Local proportionality requires that each agent prefer their allocation to the average of their neighbors' allocations in some undirected social network. It is a weaker fairness notion than envy-freeness, which also has query complexity $Ω(n^2)$, and generally incomparable to proportionality, which has query complexity $Θ(n \log n)$. This result separates the complexity of local proportionality from that of ordinary proportionality, confirming the intuition that finding a locally proportional allocation is a more difficult computational problem.

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Jamie Tucker-Foltz. 2022-11-01. Thou Shalt Covet The Average Of Thy Neighbors' Cakes. https://arxiv.org/abs/2106.11178

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