An impossibility theorem concerning positive involvement in voting

Wesley H. Holliday

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Abstract: In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet methods, namely that the choice of winners depends only on the ordering of majority margins by size.

Date: 2024-01, Revised 2025-03
New Economics Papers: this item is included in nep-cdm and nep-mic
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Published in Economics Letters, Vol. 236, March 2024, 111589

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