Neutral veto correspondences with a continuum of alternatives

Abdou, Joseph

doi:10.1007/bf01254544

Cited by 7 publications

(13 citation statements)

References 12 publications

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“…For g: An--->A, by permutation of strategies and outcomes (the reader is referred to Hurwicz and Schmeidler (1978) Remark. ACI is called almost additivity in Danilov and Sotskov (1989), y-subadditivity in Abdou (1988), and *-subadditivity in Abdou and Keiding (1991). In the context of maximality, ACI is equivalent to subadditivity.…”

Section: Citizen Sovereignty (Cs) G: S---a Satisfies Cs If G (S) --Amentioning

confidence: 99%

Strongly consistent game forms

1994

Soc Choice Welfare

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This paper characterizes strongly consistent game forms in terms of power structure and cardinality (i.e. the number of persons, alternatives or strategies). There are three main new results in this paper. First, I give a necessary condition for a game form to be strongly consistent; it is also sufficient in several cases. Second, from the view point of informational requirements and based on the first result, I give a sharp lower bound on the cardinality of each agent's strategy space, for a game form to be strongly consistent and individually rational. Third, I show that the unanimous rule is the unique game form that attains this lower bound for strong implementation of the individually rational Pareto correspondence.

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Section: Citizen Sovereignty (Cs) G: S---a Satisfies Cs If G (S) --Amentioning

confidence: 99%

Strongly consistent game forms

1994

Soc Choice Welfare

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“…[15]. Mimicking the properties of a simple game we speak of interval simple games for real-valued decisions in [0,1]. A generalization of the Shapley-Shubik index to that context was proposed in [20].…”

Section: Introductionmentioning

confidence: 99%

“…Models of influence for a continuum of actions have e.g. been studied in [1,17]. For aggregation functions there is a known generalization of the (Penrose-)Banzhaf index [15], see also [22] for more details on the relationship.…”

Section: Introductionmentioning

confidence: 99%

An Axiomatization of the Shapley-Shubik Index for Interval Decisions

2019

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The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval in the input and output. In the limit we have a continuum of options. For these games with interval decisions we prove an axiomatization of a power measure and show that the Shapley-Shubik index for simple games, as well as for (j, k) simple games, occurs as a special discretization. This relation and the closeness of the stated axiomatization to the classical case suggests to speak of the Shapley-Shubik index for games with interval decisions, that can also be generalized to a value.

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“…One of the early papers on topological effectivity functions is Keiding (1986). Our results on topological effectivity functions are motivated, in particular, by Abdou (1988). The much stronger condition of acceptability of a game form, implying not only Nash consistency but also Pareto optimality of any Nash equilibrium outcome, is studied by Hurwicz and Schmeidler (1978) and Dutta (1984).…”

Section: Introductionmentioning

confidence: 99%

Nash consistent representation of constitutions: a reaction to the Gibbard paradox

Peleg

Peters

Storcken

2002

Mathematical Social Sciences

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Neutral veto correspondences with a continuum of alternatives

Cited by 7 publications

References 12 publications

Strongly consistent game forms

Strongly consistent game forms

An Axiomatization of the Shapley-Shubik Index for Interval Decisions

Nash consistent representation of constitutions: a reaction to the Gibbard paradox

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