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

Mihir Bhattacharya and Ojasvi Khare

Papers from arXiv.org

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.

Date: 2026-06
New Economics Papers: this item is included in nep-des and nep-mic
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