No Show Paradox in Condorcet k-voting Procedures

Pérez, Joaquín; Jimeno, José L.; García, Estefanía

doi:10.1007/s10726-010-9191-9

Cited by 9 publications

(7 citation statements)

References 6 publications

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“…Both of these questions are addressed in our paper. Pérez, Jimeno, and García (2010) and Pérez, Jimeno, and García (2015) revisited participation for the optimist extension with varying notions of Condorcet-consistency. Pérez et al (2010) derived incompatibilities using a set-valued variant of Condorcet-consistency for irresolute SCFs that always select exactly k alternatives.…”

Section: Related Workmentioning

confidence: 99%

“…Pérez, Jimeno, and García (2010) and Pérez, Jimeno, and García (2015) revisited participation for the optimist extension with varying notions of Condorcet-consistency. Pérez et al (2010) derived incompatibilities using a set-valued variant of Condorcet-consistency for irresolute SCFs that always select exactly k alternatives. Inspired by early work by Holzman (1988) on resolute SCFs, Pérez et al (2015) showed that participation is compatible with Condorcet-consistency if Condorcet winners need the support of a supermajority rather than a simple majority.…”

Section: Related Workmentioning

confidence: 99%

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Strategic Abstention based on Preference Extensions: Positive Results and Computer-Generated Impossibilities

Brandl

Brandt

Geist

et al. 2019

jair

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Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining from an election. We study strategic abstention for set-valued voting rules based on Kelly's and Fishburn's preference extensions. Our contribution is twofold. First, we show that, whenever there are at least five alternatives and seven agents, every Pareto-optimal majoritarian voting rule suffers from the no-show paradox with respect to Fishburn's extension. This is achieved by reducing the statement to a finite - yet very large - problem, which is encoded as a formula in propositional logic and then shown to be unsatisfiable by a SAT solver. We also provide a human-readable proof which we extracted from a minimal unsatisfiable core of the formula. Secondly, we prove that every voting rule that satisfies two natural conditions cannot be manipulated by strategic abstention with respect to Kelly's extension and give examples of well-known Pareto-optimal majoritarian voting rules that meet these requirements.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Strategic Abstention based on Preference Extensions: Positive Results and Computer-Generated Impossibilities

Brandl

Brandt

Geist

et al. 2019

jair

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“…The motivation is different for a strategic protest vote, and the support given by abstaining is tenuously different from one of the most important monotonicity paradoxes revealed by Plassmann and Tideman (), Nurmi (), and Felsenthal () as a conditional paradox: the no‐show paradox (Fishburn and Brams ), also known as the extreme truncation paradox (see Brams ), or the abstention paradox (Pérez, Jimeno, and García ). This paradox states that the removal of a ballot or the absence of a voter might change the outcome of an election to a more preferable choice for that voter than if he or she decided to vote sincerely according to his/her preferences.…”

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confidence: 89%

Invalid Votes, Deliberate Abstentions, and the Brazilian Crisis of Representation

Nepomuceno

Costa

2019

Politics & Policy

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August 31, 2016 registered the historical impeachment of Brazilian president, Dilma Rousseff, indicted for contravening the budget law and misstating the public deficit that propelled the country into deep economic recession. Many disagreements on this matter have permeated the country’s conflict atmosphere, supported by arguments that the collective will of more than 54 million voters was disrespected. Based on 3,010 interviews conducted in 204 Brazilian cities, we construct a pairwise comparison to present arguments that Rousseff had no legitimate representation in the 2014 national elections. We demonstrate how the suboptimal support of invalid votes and deliberate abstentions might have misrepresented the results of Brazilian presidential election by choosing a pseudo‐Condorcet loser candidate. The results in the Brazilian case study presented here point to the weakness in the social process of aggregating preferences by relative or absolute majority, and sets out recommendations. Related Articles Galatas, Steven. 2008. “‘None of the Above?’ Casting Blank Ballots in Ontario Provincial Elections.” Politics & Policy 36 (3): 448‐473. https://doi.org/10.1111/j.1747-1346.2008.00116.x Stockemer, Daniel. 2013. “Corruption and Turnout in Presidential Elections: A Macro‐Level Quantitative Analysis.” Politics & Policy 41 (2): 189‐212. https://doi.org/10.1111/polp.12012 Stockemer, Daniel, and Stephanie Parent. 2014. “The Inequality Turnout Nexus: New Evidence from Presidential Elections.” Politics & Policy 42 (2): 221‐245. https://doi.org/10.1111/polp.12067 Related Media The Conversation. 2017. “Kenneth Arrow’s Legacy and Why Elections Can Be Flawed.” March 1. https://theconversation.com/kenneth-arrows-legacy-and-why-elections-can-be-flawed-73675

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“…4 Without being exhaustive, we can list Arrow and Hurwicz (1972), Packard (1979), Nitzan and Pattanaik (1984), Pattanaik and Peleg (1984), Barberà et al (1984), Pérez et al (2012).…”

Section: The Extension Rulementioning

confidence: 99%