arXiv subjects

Mihir Bhattacharya

Publications and source records attributed to Mihir Bhattacharya.

4 recordsLinked to original sources

arXiv2026

Strategy-Proof Set-Valued Choice on Single-Dipped Domains

We study strategy-proof social choice where agents have single-dipped preferences and outcomes may be sets of alternatives. While point-valued strategy-proof rules select an endpoint, we ask which outcomes survive when sets are compared through responsive extensions. Under the standard responsive extension, preferences over fixed-length intervals remain single-dipped, so the endpoint restriction persists and anonymity yields a single-threshold rule. Under responsive dominance, the incomplete order shared by all responsive extensions, an interior interval can survive because the two extreme intervals need not be comparable. For arbitrary sets, requiring every chosen alternative to be most preferred by some agent yields voting-by-committees rules, with one committee per endpoint; anonymous rules have a two-threshold quota form. The characterization holds on the entire endpoint-peaked domain, and every such rule is group-strategy-proof.

econ.TH↗

arXiv2026

Stable Matching with Choice Correspondences: Beyond Path Independence

We study stable matching with agents' choice correspondences as primitives. For many-to-many markets we introduce Individually Rational Persistence (IRP), which admits status-quo persistence, and show that substitutability (SUB) and IRP guarantee a stable matching; the constructive proof yields a symmetric matching algorithm with no proposing side and long-term contracts. For one-to-one markets we introduce replacement-based stability and show that SUB together with binary acyclicity (BA) guarantees existence. Combining the two, in the many-to-one setting, where SUB and irrelevance of rejected contracts (IRC) guarantee stability, we show that SUB with IRP on firms and BA on workers guarantees existence. We show that, in the presence of SUB, IRC is not necessary for existence in any of the three models, so stable matchings exist outside the domain of path independence.

econ.TH↗

arXiv2026

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

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.

econ.TH↗

arXiv2026

A simple characterization of single-peaked domains

This paper characterizes the single-peaked domain on a tree via the strategy-proofness of extreme rules defined on that tree. For any tree, these rules are unanimous and anonymous on any preference domain. In particular, we show that they are strategy-proof only on the single-peaked domain associated with that tree.

econ.TH↗