Single-Peakedness Does Not Prevent Leapfrogging under Abstention
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913160355643392 |
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| author | Ray, Aman Pai, Srikanth B. |
| author_facet | Ray, Aman Pai, Srikanth B. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25131 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Single-Peakedness Does Not Prevent Leapfrogging under Abstention Ray, Aman Pai, Srikanth B. Theoretical Economics 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. |
| title | Single-Peakedness Does Not Prevent Leapfrogging under Abstention |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2605.25131 |