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arXiv · 2605.23742

Super Condorcet Winners and Limit Coalitional Manipulability of IRV

François Durand·Élie de Panafieu·Guillem Perarnau
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Abstract

We study the limit CM rate of single-winner voting rules under Impartial Culture, defined as the probability that a preference profile is coalitionally manipulable in the limit of large electorates. For m = 3 candidates, Lepelley and Valognes [1999] derived a closed-form expression for Plurality with Runoff, or equivalently Instant-Runoff Voting (IRV), and showed that its limit CM rate is strictly below 1. This is remarkable because Kim and Roush [1996] established a limit of 1 for several major rules, including Maximin and all positional scoring rules except Veto. In this paper, we generalize the result of Lepelley and Valognes to any number of candidates m $\ge$ 4. We show that Plurality with Runoff has a limit CM rate equal to 1 for all m $\ge$ 4, whereas IRV retains a limit CM rate strictly below 1. To this end, we rely on the notion of Super Condorcet Winner, recently introduced by Durand [2025], which yields an upper bound on the CM rate of IRV. We prove that this bound is asymptotically tight and compute the probability that a Super Condorcet Winner exists, thereby obtaining the exact limit CM rate of IRV.

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BibTeXRIS

François Durand, Élie de Panafieu, Guillem Perarnau. 2026-05-22. Super Condorcet Winners and Limit Coalitional Manipulability of IRV. https://arxiv.org/abs/2605.23742

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