Dis&amp;approval voting: a characterization

Alcantud, José Carlos R.; Laruelle, Annick

doi:10.1007/s00355-013-0766-7

Cited by 69 publications

(27 citation statements)

References 22 publications

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“…I show that Evaluative Voting can be characterized by a simple measurability assumption for arbitrary finite evaluation sets. This result is thus broader than the characterizations of Evaluative Voting obtained for three evaluations (Alcantud and Laruelle, 2013) and for numerical evaluations (Gaertner and Xu, 2012).…”

Section: Introductionmentioning

confidence: 64%

Voting with evaluations: Characterizations of evaluative voting and range voting

Macé

2018

Journal of Mathematical Economics

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I conduct an axiomatic analysis of voting rules in a context where voters evaluate each candidate by assigning her an evaluation from a pre-established set. I focus on additive rules, which follow the utilitarian paradigm. Characterization results are provided for each of the two prominent additive rules: Evaluative Voting when the evaluation set is finite and Range Voting when the evaluation set is [0, 1].

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Section: Introductionmentioning

confidence: 64%

Voting with evaluations: Characterizations of evaluative voting and range voting

Macé

2018

Journal of Mathematical Economics

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“…While we only studied a specific voting procedure, it seems meaningful to extend this type of analysis to other voting methods, at the very least because the absence of agreement as per what type of information is to be asked to voters, or used in social choice procedures, seems to call for a formal treatment thereof. For instance, this could help elucidate the consequences of replacing the dichotomous informational basis of Approval Voting with a trichotomous one -allowing voters to express approval, disapproval and neutrality towards candidates -as required by an alternative to Approval Voting, the dis&approval voting procedure, that has received some attention in recent years (see Hillinger (2005), Alcantud and Laruelle (2014) or Gonzalez et al (2019)).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

A Characterization of Approval Voting Without the Approval Balloting Assumption

Ceron

Gonzalez²

2019

SSRN Journal

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We provide an axiomatic characterization of Approval Voting without the approval balloting assumption. The dichotomous structure of the informational basis of Approval voting as well as its aggregative rationale are jointly derived from a set of normative conditions on the voting procedure. The first one is the wellknown social-theoretic principle of consistency; the second one, ballot richness, requires voters to be able to express a sufficiently rich set of opinions; the last one, dubbed no single-voter overrides, demands that the addition of a voter to an electorate cannot radically change the outcome of the election. Such result is promising insofar it suggests that the informational basis of voting may have a normative relevance that deserves formal treatment. AbstractWe provide an axiomatic characterization of Approval Voting without the approval balloting assumption. The dichotomous structure of the informational basis of Approval voting as well as its aggregative rationale are jointly derived from a set of normative conditions on the voting procedure. The first one is the well-known social-theoretic principle of consistency; the second one, ballot richness, requires voters to be able to express a sufficiently rich set of opinions; the last one, dubbed no single-voter overrides, demands that the addition of a voter to an electorate cannot radically change the outcome of the election. Such result is promising insofar it suggests that the informational basis of voting may have a normative relevance that deserves formal treatment. for very useful comments that greatly improved this paper. All remaining errors are our own. † federica.ceron@univ-paris1.fr ‡ stephane.gonzalez@univ-st-etienne.fr § Financial support of IDEXLYON from Université de Lyon (project INDEPTH) within the Programme Investissements d'Avenir (ANR-16-IDEX-0005) is gratefully acknowledged.

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“…For instance, if A = (t A , f A ) = (0.5, 0.2), it can be interpreted as "the vote for the resolution is 5 in favor, 2 against, and 3 abstentions" [6]. Based on this ternary voting model, the membership degree of an IFV reveals the percentage of approval votes, the nonmembership degree reflects the rejection rate, and the indeterminacy can be considered as the abstention rate [20]. With this interpretation in mind, one can see that the whole triangle region, with (0, 1), (0, 0) and (1, 0) as its vertices, constitutes all possible outcomes from a vote.…”

Section: Centroid Transformations Of Intuitionistic Fuzzy Valuesmentioning

confidence: 99%

Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

et al. 2018

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Atanassov’s intuitionistic fuzzy sets extend the notion of fuzzy sets. In addition to Zadeh’s membership function, a non-membership function is also considered. Intuitionistic fuzzy values play a crucial role in both theoretical and practical progress of intuitionistic fuzzy sets. This study introduces and explores various types of centroid transformations of intuitionistic fuzzy values. First, we present some new concepts for intuitionistic fuzzy values, including upper determinations, lower determinations, spectrum triangles, simple intuitionistic fuzzy averaging operators and simply weighted intuitionistic fuzzy averaging operators. With the aid of these notions, we construct centroid transformations, weighted centroid transformations, simple centroid transformations and simply weighted centroid transformations. We provide some basic characterizations regarding various types of centroid transformations, and show their difference using an illustrating example. Finally, we focus on simple centroid transformations and investigate the limit properties of simple centroid transformation sequences. Among other facts, we show that a simple centroid transformation sequence converges to the simple intuitionistic fuzzy average of the lower and upper determinations of the first intuitionistic fuzzy value in the sequence.

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Dis&approval voting: a characterization

Cited by 69 publications

References 22 publications

Voting with evaluations: Characterizations of evaluative voting and range voting

Voting with evaluations: Characterizations of evaluative voting and range voting

A Characterization of Approval Voting Without the Approval Balloting Assumption

Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators

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