Condorcet Efficiency and Social Homogeneity

Gehrlein, William V.; Lepelley, Dominique

doi:10.1007/978-3-642-03107-6_5

Cited by 5 publications

(5 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This observation gives strong support to H2 with regard to plurality rule. Some obstacles to believe the general veracity of H2 started to become visible in Gehrlein (1995) when some other common voting rules were found to have the exact opposite results that were observed with plurality rule, behaving in a fashion that was quite contrary to the general notions in H2. Some explanations were given in an attempt to explain the observations that were made.…”

Section: Previous Conflicting Evidence Related To H2mentioning

confidence: 84%

“…Berg and Bjurulf (1983) argue that any differences between IC and IAC become insignificant for m ≥ 5, and the findings of Lepelley et al (2000) reflect this by showing inconclusive results when comparing CE PR (m, ∞|P E(1)) and CE PR (m, ∞|P E(0)) for m > 6. Lepelley et al (2000b) and Gehrlein (1995Gehrlein ( , 2003a obtain computed values of CE PR (3, n| P E(α)) for various odd n and for numerous values of α to show that CE PR (3, n|P E(α)) consistently increases as α increases for any given odd n.…”

Section: Previous Conflicting Evidence Related To H2mentioning

confidence: 96%

See 1 more Smart Citation

The Unexpected Behavior of Plurality Rule

Gehrlein¹,

Lepelley²

2008

Theory Decis

Self Cite

View full text Add to dashboard Cite

International audienceWhen voters’ preferences on candidates are mutually coherent, in the sense that they are at all close to being perfectly single-peaked, perfectly single-troughed, or perfectly polarized, there is a large probability that a Condorcet Winner exists in elections with a small number of candidates. Given this fact, the study develops representations for Condorcet Efficiency of plurality rule as a function of the proximity of voters’ preferences on candidates to being perfectly single-peaked, perfectly single-troughed or perfectly polarized. We find that the widely used plurality rule has Condorcet Efficiency values that behave in very different ways under each of these three models of mutual coherence

show abstract

Section: Previous Conflicting Evidence Related To H2mentioning

confidence: 84%

Section: Previous Conflicting Evidence Related To H2mentioning

confidence: 96%

The Unexpected Behavior of Plurality Rule

Gehrlein¹,

Lepelley²

2008

Theory Decis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Generally speaking, there are two different measures of homogeneity widely appealed to in the literature, one relying on Abrams's (1976) definition, which tracks the degree of agreement on particular preference orderings, and another relying on Kendall's coefficient of concordance (Fishburn, 1973), which tracks the degree of deviation from an impartial culture towards what is called a purely arbitrary culture, which is defined as a population with perfect agreement on one preference ordering. Gehrlein (1987;1995) and Gehrlein and Lepelly (2011: 191-194) show that, once we start introducing homogeneity of both kinds defined above, then (i) several major social choice mechanisms begin increasing in convergence as the level of homogeneity increases and (ii) this convergence increases still as population size increases. Indeed, once the population size gets large enough then, given the introduction of some homogeneity, we should see perfect convergence of social choice mechanisms.…”

Section: Homogeneity and Convergencementioning

confidence: 99%

Aggregating out of indeterminacy

Kogelmann

2017

Politics, Philosophy & Economics

View full text Add to dashboard Cite

This article explores public reason liberalism's indeterminacy problem, a problem that obtains when we admit significant diversity into our justificatory model. The article argues first that Gerald Gaus's solution to the indeterminacy problem is unsatisfactory and second that, contra Gaus's concerns, social choice theory is able to solve public reason's indeterminacy problem. Moreover, social choice theory can do so in a way that avoids the worries raised against Gaus's solution to the indeterminacy problem as well as the worries Gaus himself raises against the use of social choice mechanisms. Social choice theory thus rescues public reason liberalism by aggregating out of indeterminacy.

show abstract

“…For further information about the structure of performance functions and how we selected them, see Section 3. few if any cycles. In a meta-analysis, Van Deemen [118] and Gehrlein [41] found that roughly ten percent of 265 elections studied exhibited the paradox [117], usually among small electorates. Thus, the axiomatic theory been criticized for overstating the prevalence of voter cycles [86,88].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Cebra¹,

Strang²

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Condorcet Efficiency and Social Homogeneity

Cited by 5 publications

References 48 publications

The Unexpected Behavior of Plurality Rule

The Unexpected Behavior of Plurality Rule

Aggregating out of indeterminacy

Similarity Suppresses Cyclicity: Why Similar Competitors Form Hierarchies

Contact Info

Product

Resources

About