Single-Peakedness Does Not Prevent Leapfrogging under Abstention

Aman Ray; Srikanth B. Pai

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arXiv · 2605.25131

Single-Peakedness Does Not Prevent Leapfrogging under Abstention

Aman Ray·Srikanth B. Pai

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Abstract

Parties in spatial competition rarely choose platforms that reverse their ideological order. Mutual leapfrogging is the strongest form of reversal: each party locates beyond the other party's ideal point. In voting models without abstention single-peakedness rules out such reversals. We show that this conclusion does not survive endogenous abstention. There is a spatial voting model in which voter and party preferences are single-peaked, yet mutual leapfrogging occurs in pure-strategy equilibrium. The equilibrium survives because some deviations change which voters participate. We prove that such equilibria are impossible under a sufficient ordinal condition: parties agree on how to rank leftward and rightward deviations from their ideal points. The condition is general enough to cover symmetric single-peaked utilities and common translated utility shapes.

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Aman Ray, Srikanth B. Pai. 2026-05-24. Single-Peakedness Does Not Prevent Leapfrogging under Abstention. https://arxiv.org/abs/2605.25131

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