The forgotten decision rules: Majority rules based on difference of votes

Llamazares, Bonifacio

doi:10.1016/j.mathsocsci.2005.12.001

Cited by 50 publications

(62 citation statements)

References 17 publications

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“…Assuming a required difference in support k equal to 1.75 and applying the corresponding M 1.75 majority we have In this framework, the concept of majorities based on difference of votes was introduced in García-Lapresta and Llamazares (2001) and was later axiomatically characterized in Llamazares (2006), and subsequently in Houy (2007). Under these majorities, an alternative, say x i , is declared the winner if the number of individuals who prefer that alternative, to the other one, say x j , exceeds the number of individuals who prefer x j to x i in a difference of votes, fixed before the election process.…”

Section: Consider the Profile (Rmentioning

confidence: 99%

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Diss

Pérez-Asurmendi

2016

Group Decis Negot

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Computer simulations are used to evaluate the likelihood of consistent outcomes under the class of majorities based on difference in support. These majorities require certain consensus in collective preferences to declare an alternative as the winner. More precisely, individuals show preference intensities in the unit interval among each pair of alternatives and it is required that the winner alternative obtains a difference in the sum of the intensities with respect to the loser alternative. This difference is a real number located between 0 and the total number of voters. We introduce the values of the required threshold for which majorities based on difference in support lead to transitive and triple-acyclic collective decisions with a probability of 1. Our results improve the previous theoretical ones since they require softer thresholds to reach consistent collective decisions.

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Section: Consider the Profile (Rmentioning

confidence: 99%

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Diss

Pérez-Asurmendi

2016

Group Decis Negot

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“…The concept and the definition of majorities based on difference of votes was introduced in García-Lapresta and Llamazares (2001) and was later axiomatically characterized in Llamazares (2006), and subsequently in Houy (2007). These rules involve crisp preferences, i.e.…”

Section: Majorities Based On Difference Of Votesmentioning

confidence: 99%

“…This paper is devoted to analyze and compare the probabilities of consistent collective decisions over three alternatives for a class of majorities rules: majorities based on difference of votes (García-Lapresta and Llamazares 2001;Llamazares 2006;Houy 2007). Given two alternatives, these majorities based on differences focus on requiring to an alternative, to be declared the winner, to reach a number of votes that exceeds the number of votes for the other alternative in a quantity fixed before the voting process.…”

mentioning

confidence: 99%

Consistent collective decisions under majorities based on difference of votes

Diss

Pérez-Asurmendi

2015

Theory Decis

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The main criticism to the aggregation of individual preferences under majority rules refers to the possibility of reaching inconsistent collective decisions from the election process. In these cases, the collective preference includes cycles and even could prevent the election of any alternative as the collective choice. The likelihood of consistent outcomes under a class of majority rules constitutes the aim of this paper. Specifically, we focus on majority rules that require certain consensus in individual preferences to declare an alternative as the winner. Under majorities based on difference of votes, the requirement asks to the winner alternative to obtain a difference in votes with respect to the loser alternative taking into account that individuals are endowed with weak preference orderings. Same requirement is asked to the restriction of these rules to individual linear preferences.

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“…The adoption of this principle leads to the unanimity rule. In between, there are the different versions of the absolute majority rule, where enough support means having the support of some percentage p > 50% of the individuals; see Llamazares (2006) and Houy (2007) for characterizations of absolute majority rules.…”

Section: Introductionmentioning

confidence: 99%

Parallel axiomatizations of majority and unanimity

Quesada

2011

Economics Letters

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The relative majority rule and the unanimity rule are characterized for the case in which there are only two alternatives. The main axioms are motivated by a principle of binary representativeness: the aggregation of the preferences of n voters is the result of splitting the n voters into two groups, aggregating the preferences of the voters of each group, selecting for each group a representative that adopts the preference of the group, and finally aggregating the preferences of the two representatives. The two characterizations are shown to differ from each other in just one axiom, expressing strategyproofness (unanimity) or group strategyproofness (majority).

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The forgotten decision rules: Majority rules based on difference of votes

Cited by 50 publications

References 17 publications

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Consistent collective decisions under majorities based on difference of votes

Parallel axiomatizations of majority and unanimity

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