Fair Division of a Heterogeneous Good Between Two Agents: An Ordinal Approach

Mihir Bhattacharya; Ojasvi Khare

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arXiv · 2606.06059

Fair Division of a Heterogeneous Good Between Two Agents: An Ordinal Approach

Mihir Bhattacharya·Ojasvi Khare

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Abstract

We study the division of a heterogeneous good between two agents into contiguous bundles, each defined by a starting location and a quantity, in a purely ordinal framework that does not rely on cardinal valuations. We introduce a general class of monotonic preferences representable by indifference curves. We show that an allocation is Pareto efficient and envy-free if and only if it lies in a specific ``balanced region'', implying that an equal split is fair only when it belongs to this region. We further show that no rule can simultaneously satisfy Pareto efficiency, envy-freeness, and strategy-proofness.

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Mihir Bhattacharya, Ojasvi Khare. 2026-06-04. Fair Division of a Heterogeneous Good Between Two Agents: An Ordinal Approach. https://arxiv.org/abs/2606.06059

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