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arXiv · 2509.15812

Diversity of Structured Domains via k-Kemeny Scores

Piotr Faliszewski·Krzysztof Sornat·Stanisław Szufa·Tomasz Wąs
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Abstract

In the k-Kemeny problem, we are given an ordinal election, i.e., a collection of votes ranking the candidates from best to worst, and we seek the smallest number of swaps of adjacent candidates that ensure that the election has at most k different rankings. We study this problem for a number of structured domains, including the single-peaked, single-crossing, group-separable, and Euclidean ones. We obtain two kinds of results: (1) We show that k-Kemeny remains intractable under most of these domains, even for k=2, and (2) we use k-Kemeny to rank these domains in terms of their diversity.

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Piotr Faliszewski, Krzysztof Sornat, Stanisław Szufa, Tomasz Wąs. 2025-09-19. Diversity of Structured Domains via k-Kemeny Scores. https://arxiv.org/abs/2509.15812

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