The incompatibility of the Condorcet winner and loser criteria with positive involvement and resolvability
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918345662529536 |
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| author | Holliday, Wesley H. |
| author_facet | Holliday, Wesley H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10506 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The incompatibility of the Condorcet winner and loser criteria with positive involvement and resolvability Holliday, Wesley H. Theoretical Economics Computer Science and Game Theory Multiagent Systems 91B12, 91B14, 91B10 I.2.11 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. |
| title | The incompatibility of the Condorcet winner and loser criteria with positive involvement and resolvability |
| topic | Theoretical Economics Computer Science and Game Theory Multiagent Systems 91B12, 91B14, 91B10 I.2.11 |
| url | https://arxiv.org/abs/2601.10506 |