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

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  • Mihir Bhattacharya
  • Ojasvi Khare

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. "Fair Division of a Heterogeneous Good Between Two Agents: An Ordinal Approach," Papers 2606.06059, arXiv.org.
    • Handle: RePEc:arx:papers:2606.06059
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    References listed on IDEAS

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    3. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
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