On the empirical relevance of Condorcet’s paradox

Deemen, Adrian Van

doi:10.1007/s11127-013-0133-3

Cited by 23 publications

(13 citation statements)

References 70 publications

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“…Cycles in opinion play an important role in social choice theory. When aggregate voter opinions involving the top candidates are cyclic, no election system can guarantee that the winner fairly reflects the majority opinion [3,117]. Such cycles can occur even if each voter's preferences are well ordered.…”

Section: Introduction 1motivationmentioning

confidence: 99%

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Cebra¹,

Strang²

2022

Preprint

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Competitive systems can exhibit both hierarchical (transitive) and cyclic (intransitive) structures. Despite theoretical interest in cyclic competition, which offers richer dynamics, and occupies a larger subset of the space of possible competitive systems, most real-world systems are predominantly transitive. Why? Here, we introduce a generic mechanism which promotes transitivity, even when there is ample room for cyclicity. Consider a competitive system where outcomes are mediated by competitor attributes via a performance function. We demonstrate that, if competitive outcomes depend smoothly on competitor attributes, then similar competitors compete transitively. We quantify the rate of convergence to transitivity given the similarity of the competitors and the smoothness of the performance function. Thus, we prove the adage regarding apples and oranges. Similar objects admit well ordered comparisons. Diverse objects may not. To test that theory, we run a series of evolution experiments designed to mimic genetic training algorithms. We consider a series of canonical bimatrix games and an ensemble of random performance functions that demonstrate the generality of our mechanism, even when faced with highly cyclic games. We vary the training parameters controlling the evolution process, and the shape parameters controlling the performance function, to evaluate the robustness of our results. These experiments illustrate that, if competitors evolve to optimize performance, then their traits may converge, leading to transitivity.

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Section: Introduction 1motivationmentioning

confidence: 99%

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Cebra¹,

Strang²

2022

Preprint

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“…Because of the limited knowledge of a single expert, multiple experts are often required to analyse some particular subject to help governments, businesses, and other organizations make optimal choices, and this is called group assessment or group decision‐making (Lourenzutti, Krohling, & Reformat, 2017; Skorupski, 2015; Tchangani, 2007; Wang, 2011). In previously conducted research works, it was suggested that the reliability of group assessment is higher than that of individual judgement (Zhang & Lu; Charness & Levin, 2007; Koriat, 2012; Deemen, 2014; Awad, Caminada, Pigozzi, Podlaszewski, et al, 2017), where the reliability denotes the distance between the true value and an estimate of the assessment object. However, the reliability of group‐assessment results is influenced by multiple factors, such as the indicators of the assessment, methods for the elicitation and aggregation of expert opinions, and calibration and the judgement ability of experts (Cooke, 1991; Clemen & Winkler, 1999; European Food Safety Authority, 2014; Colson & Cooke, 2017).…”

Section: Introductimentioning

confidence: 99%

Authority updating: An expert authority evaluation algorithm considering post‐evaluation and power indices in social networks

Shi

Guo

2020

Expert Systems

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In group assessment, the focus is on finding high-authority experts to improve the reliability of assessment results. In this study, we propose an authority updating algorithm while considering the power and judgement reliability of an expert on the basis of social networks and post-evaluations. A network power index is established and used to reflect the power of an expert while considering social networks. The measurement of the judgement reliability of an expert considers the post-evaluation of the objects selected by experts, thereby more scientifically reflecting the reliability of experts. The analysis shows the following: although the social-network structure influences the authority of experts, the influence weakens when the assessment group is a highly or even fully connected group; the network effect may increase the authority of some experts and reduce that of others, and it will weaken as the network connectivity increases; moreover, the judgement reliability and authority of an expert while considering post-evaluation can encourage him/her to make fair assessments and strive to reduce his/her motivation and cognitive biases.

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“…Thus an important area of research has been to identify how often there occur cycles in the margin graph, both in historical situations and theoretically under various assumptions on the voters. Riker [Rik58] argues that various amendments in the Agricultural Appropriation Act of 1953 in the US House of Representatives formed a cycle; Bjurulf and Niemi [BN78] found similar situations in the Swedish parliament; Stensholt [Ste99] found a cycle in a decision by the Norwegian national assembly; see also Van Deemen [Dee14], Kurrild-Klitgaard [KK01], and Truchon [Tru98].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of Random Elections with Large Numbers of Voters

Harrison-Trainor¹

2020

Preprint

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In an election in which each voter ranks all of the candidates, we consider the headto-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each candidate over each of the other candidates. A central issue in developing voting methods is that there can be cycles in this graph, where candidate A defeats candidate B, B defeats C, and C defeats A. In this paper we apply the central limit theorem, graph homology, and linear algebra to analyze how likely such situations are to occur for large numbers of voters. There is a large literature on analyzing the probability of having a majority winner; our analysis is more fine-grained. The result of our analysis is that in elections with the number of voters going to infinity, margin graphs that are more cyclic in a certain precise sense are less likely to occur. * We thank Wesley Holliday and Eric Pacuit for extensive comments and discussions.

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On the empirical relevance of Condorcet’s paradox

Cited by 23 publications

References 70 publications

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Authority updating: An expert authority evaluation algorithm considering post‐evaluation and power indices in social networks

An Analysis of Random Elections with Large Numbers of Voters

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