May’s theorem in an infinite setting

Surekha, K.; Rao, K. P. S. Bhaskara

doi:10.1016/j.jmateco.2009.06.012

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…This problem leads us to studying finitely additive measures which extend the asymptotic density and are defined for all subsets of N. Such measures are called density measures and they were studied by several authors, for example [3,18,22,26]. Density measures (and other types of densities on N) have applications, for example, in theory of social choice [8,17,25].…”

Section: Introductionmentioning

confidence: 99%

Extreme points of the set of density measures

Letavaj¹,

Mišík²,

Sleziak³

2015

Journal of Mathematical Analysis and Applications

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Abstract. We study finitely additive measures on the set N which extend the asymptotic density (density measures). We show that there is a one-toone correspondence between density measures and positive functionals in ℓ * ∞ , which extend Cesàro mean. Then we study maximal possible value attained by a density measure for a given set A and the corresponding question for the positive functionals extending Cesàro mean. Using the obtained results, we can find a set of functionals such that their closed convex hull in ℓ * ∞ with weak * topology is precisely the set of all positive functionals extending Cesàro mean. This also describes a set of density measures, from which all density measures can be obtained as the closed convex hull.

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Section: Introductionmentioning

confidence: 99%

Extreme points of the set of density measures

Letavaj¹,

Mišík²,

Sleziak³

2015

Journal of Mathematical Analysis and Applications

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“…For example, we could allow the size of the voting population to be the cardinality of R, the real numbers. For more information on this model see the article by K. Surekha and K.P.S Bhaskara Rao [18].…”

Section: Chapter 7 Remarks and Conclusionmentioning

confidence: 99%

“…18) holds. If k > −n, then, by Case 2 in the proof of Theorem 4, l = n − 1 andf (π ′′ ) ≤ 0 for all π ′′ belonging to U − .…”

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confidence: 92%

Extending difference of votes rules on three voting models.

King¹

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In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any nonnegative integer k, the difference of votes rule M k outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. In addition, we state and prove Llamazares' theorem in voting models where either there is an infinite number of votes or each voter is allowed to express an intensity level for one alternative over the other. Finally, we will use a computer simulation to compare different voting methods to simple majority rule, in order to analyze the probability that the voting rules would output different results. v TABLE OF CONTENTS

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Acyclicity, anonymity, and prefilters

Bossert

Cato

2020

Journal of Mathematical Economics

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May’s theorem in an infinite setting

Cited by 5 publications

References 7 publications

Extreme points of the set of density measures

Extreme points of the set of density measures

Extending difference of votes rules on three voting models.

Acyclicity, anonymity, and prefilters

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