Achievable hierarchies in voting games with abstention

Freixas, Josep; Tchantcho, Bertrand; Tedjeugang, Narcisse

doi:10.1016/j.ejor.2013.11.030

Cited by 16 publications

(5 citation statements)

References 29 publications

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“…20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64Examples of the treatment of the importance of rankings in these different contexts can be found in: [Alonso-Meijide 2009, Bishnu 2012, Cook 2006, Freixas et al 2014a, Jones et al 2010, Levitin 2003, Obata et al 2003]. …”

Section: Resultsmentioning

confidence: 99%

“…Furthermore I Y A respects the D Y A -desirability relation, I AN respects the D AN -desirability relation, and I Y N respects the D Y N -desirability relation, the three desirability relations are introduced in [Freixas et al 2014a] and are of fundamental importance for the consistency of the notion of weighted voting rule with abstention. The D Y A -desirability relation formalizes the intuitive notion that is the basis of the expression: "p has at least as Y A-power as r" and it is formalized in terms of the formation of winning tripartition when swamping the voter from the abstention level to the yes level.…”

Section: As Illustrated Inmentioning

confidence: 99%

See 1 more Smart Citation

Power in voting rules with abstention: an axiomatization of a two components power index

Freixas

Lucchetti

2016

Ann Oper Res

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Abstract:In order to study voting situations when voters can also abstain and the output can be only binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf's index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationPower in voting rules with abstention: an axiomatization of a two components power index Abstract: In order to study voting situations when voters can also abstain and the output can be only binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf's index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.

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Section: Resultsmentioning

confidence: 99%

Section: As Illustrated Inmentioning

confidence: 99%

Power in voting rules with abstention: an axiomatization of a two components power index

Freixas

Lucchetti

2016

Ann Oper Res

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“…In the present section we use it to extend the desirability relation to the context of (j, 2)-simple games. These notions have been extensively studied for j = 3 in [24,30,22,16,17]. As defined above their extension for j ≥ 3 become natural.…”

Section: Definition 32 {Marginal Contribution Of a Player}mentioning

confidence: 99%

A critical analysis on the notion of power

Freixas

Pons

2021

Ann Oper Res

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In this paper we discuss on several ways to extend power indices, regarded as measures of power as a payment (P-power), in the context of simple games with three or more ordered levels of input approval. Two groups of power indices for simple games are deduced from the selection of 1) a bargaining model, and 2) a set of coalitions that count to measure power. The combination of two well-known bargaining models and three subsets of winning coalitions lead to six well-known power indices for simple games as a payoff. The main purpose of the paper is to generalize this scheme to the broader context considered.We show that several notions of criticality arise when considering three or more levels of approval and we propose some natural ways to count criticality when it comes to measuring power as a payment. We highlight two of them, first-order criticality and total criticality. Thus, we establish some reasonable power indices by selecting 1) a bargaining model, 2) a set of coalitions, and 3) a way to measure criticality. In particular, we show two reasonable ways to extend well-known power indices, such as the Banzhaf, Johnston, Deegan and Packel, or Holler from simple games to games with several ordered levels of approval in the input.

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“…This important issue was solved with the concept of weighted j-simple game provided in [33]. A characterization for it in terms of trade robustness was provided there, since then several alternative works deal with the notion of weighted j-simple game, among others [34,35,36].…”

Section: An Axiomatization For the F-valuementioning

confidence: 99%

“…The last work provides a notion of weighted game endorsed by characterizations of the property of trade-robustness. Other important notions as those of the desirability relation, transitivity, acyclicity, and hierarchies, are extended in this broader context in [35,36,44,46,51].…”

Section: Introductionmentioning

confidence: 99%