Analytical representation of probabilities under the IAC condition

Huang, Haibo; Chua, Vincent

doi:10.1007/s003550050011

Cited by 38 publications

(17 citation statements)

References 4 publications

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“…2. Interestingly, this result has been re-discovered in the voting theory context by Huang and Chua (2000) for the special case of one parameter.…”

Section: Resultsmentioning

confidence: 66%

The Unexpected Behavior of Plurality Rule

Gehrlein¹,

Lepelley²

2008

Theory Decis

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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

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“…2. Interestingly, this result has been re-discovered in the voting theory context by Huang and Chua (2000) for the special case of one parameter.…”

Section: Resultsmentioning

confidence: 66%

The Unexpected Behavior of Plurality Rule

Gehrlein¹,

Lepelley²

2008

Theory Decis

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“…Roughly, the total number of anonymous profiles, that satisfy each finite set of linear inequalities with integer coefficients, can be represented by a polynomial in n and p with periodic coefficients. This is in fact a well-established result in the literature on counting the number of integer points in a lattice polytope (see Ehrhart 1962;Huang andChua 2000 or Lepelley et al 2008). Lepelley et al (2008) provide a pedagogical presentation of several computation approaches (or algorithms) while Gehrlein and Lepelley (1999) contains a detailed application of the specific method applied here.…”

Section: Computerized Evaluation Methodsmentioning

confidence: 74%

“…In order to derive our formulae, we use the technique whose origins are in Gehrlein and Fishburn (1976) and more specifically based on Ehrhart polynomials (see for example Huang andChua 2000 or Gehrlein 2002). The whole derivation process has been written as a computer program (available from the authors upon simple request) from which we obtain the total number of anonymous profiles that satisfy each set of linear inequalities obtained.…”

Section: Computerized Evaluation Methodsmentioning

confidence: 99%

The $$q$$ q -majority efficiency of positional rules

2014

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According to a given quota q, a candidate a is beaten by another candidate b if at least a proportion of q individuals prefer b to a. The q-majority efficiency of a voting rule is the probability that the rule selects a candidate who is never beaten under the q-majority, given that such a candidate exits. Closed form representations are obtained for the q-majority efficiency of positional rules (simple and sequential) in three-candidate elections. It turns out that the q-majority efficiency is: (i) significantly greater for sequential rules than for simple positional rules; and (ii) very close to the q-Condorcet efficiency, the conditional probability that a positional rule will elect the candidate who beats all others under the q-majority, when one exists.

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“…We also consider special cases, specifically when the electorate is infinitely large or when the number of sponsors arbitrarily is fixed. All of these results are derived from the inequalities describing vulnerable situations by the use of computerized evaluation processes based on the same technique as the one in Gehrlein and Fishburn (1976), Gehrlein and Lepelley (1999) or Huang and Chua (2000), under the IAC hypothesis.…”

Section: Description On Strategic Sponsoringmentioning

confidence: 99%