| A joint Politics and Economics series |
| Social choice and electoral systems |
|---|
 |
 Mathematics portal |
In social choice, a no-show paradox is a pathology in some voting rules, where a candidate loses an election as a result of having too many supporters.[1][2] More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob.[3] Voting systems without the no-show paradox are said to satisfy the participation criterion.[4]
In systems that fail the participation criterion, a voter can end up effectively disenfranchised by the electoral system, because turning out to vote would make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote.[5][6][7]
Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule[1][8] can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the randomized Condorcet rule is not affected by the pathology. The majority judgment rule fails as well, but passes a weaker condition: giving a candidate the maximum (minimum) rating can never cause them to lose (win).[9] Ranked-choice voting (RCV) and the two-round system both fail the participation criterion with high frequency in competitive elections, typically as a result of a center squeeze.[2][3][10]
The no-show paradox is similar to, but not the same as, the perverse response paradox. Perverse response happens when an existing voter can make a candidate win by decreasing their rating of that candidate (or vice-versa). For example, under ranked-choice voting, moving a candidate from first-place to last-place on a ballot can cause them to win.[11]
- ^ a b Moulin, Hervé (1988-06-01). "Condorcet's principle implies the no show paradox". Journal of Economic Theory. 45 (1): 53–64. doi:10.1016/0022-0531(88)90253-0.
- ^ a b Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN 0092-5853. JSTOR 2110496.
- ^ a b Ray, Depankar (1986-04-01). "On the practical possibility of a 'no show paradox' under the single transferable vote". Mathematical Social Sciences. 11 (2): 183–189. doi:10.1016/0165-4896(86)90024-7. ISSN 0165-4896.
- ^ Woodall, Douglas (December 1994). "Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994".
- ^ Pukelsheim, Friedrich (2014). Proportional representation : apportionment methods and their applications. Internet Archive. Cham; New York : Springer. ISBN 978-3-319-03855-1.
- ^ dpa (2013-02-22). "Bundestag beschließt neues Wahlrecht". Die Zeit (in German). ISSN 0044-2070. Retrieved 2024-05-02.
- ^ BVerfG, Urteil des Zweiten Senats vom 03. Juli 2008 - 2 BvC 1/07, 2 BvC 7/07 -, Rn. 1-145. 121 BVerfGE - 2 BvC 1/07, 2 BvC 7/07 - (BVerfG 03 July 2008). ECLI:DE:BVerfG:2008:cs20080703.2bvc000107
- ^ Brandt, Felix; Geist, Christian; Peters, Dominik (2016-01-01). "Optimal Bounds for the No-Show Paradox via SAT Solving". Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems. AAMAS '16. Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems: 314–322. arXiv:1602.08063. ISBN 9781450342391.
- ^ Markus Schulze (1998-06-12). "Regretted Turnout. Insincere = ranking". Retrieved 2011-05-14.
- ^ McCune, David; Wilson, Jennifer (2024-04-07). "The Negative Participation Paradox in Three-Candidate Instant Runoff Elections". arXiv:2403.18857 [physics.soc-ph].
- ^ Fishburn, Peter C.; Brams, Steven J. (1983-01-01). "Paradoxes of Preferential Voting". Mathematics Magazine. 56 (4): 207–214. doi:10.2307/2689808. JSTOR 2689808.