The incompatibility of the Condorcet winner and loser criteria with positive involvement and resolvability

Wesley H. Holliday

Papers from arXiv.org

Abstract: We prove that there is no preferential voting method satisfying the Condorcet winner and loser criteria, positive involvement (if a candidate $x$ wins in an initial preference profile, then adding a voter who ranks $x$ uniquely first cannot cause $x$ to lose), and $n$-voter resolvability (if $x$ initially ties for winning, then $x$ can be made the unique winner by adding some set of up to $n$ voters). This impossibility theorem holds for any positive integer $n$. It also holds if either the Condorcet loser criterion is replaced by independence of clones or positive involvement is replaced by negative involvement.

Date: 2026-01, Revised 2026-02
New Economics Papers: this item is included in nep-cdm, nep-mic and nep-pol
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