Complete simple games

Carreras, Francesc; Freixas, Josep

doi:10.1016/0165-4896(96)00815-3

Cited by 90 publications

(100 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of hierarchies within the class of simple games can be traced back to Friedman et al [20] and continued by Bean et al [3], even though it is also an implicit study in Carreras and Freixas [5]. Indeed, in Friedman et al [20] it is proved that complete simple games and, particularly, weighted simple games show many di¤erent hierarchies, although two sequences of hierarchies are never achievable.…”

Section: I-hierarchiesmentioning

confidence: 99%

Achievable hierarchies in voting games with abstention

Freixas

Tchantcho

Tedjeugang

2014

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

: It is well known that he in ‡uence relation orders the voters the same way as the classical Banzhaf and Shapley-Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the in ‡uence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of in ‡uence relation.

show abstract

Section: I-hierarchiesmentioning

confidence: 99%

Achievable hierarchies in voting games with abstention

Freixas

Tchantcho

Tedjeugang

2014

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…For additional material on simple games, the reader is referred to [3], [6], [8], [18], [19], and [21] among others. Given a simple game (N, W ), assume that a proposal P r has to be submitted to the members of an assembly N .…”

Section: Introductionmentioning

confidence: 99%

Bounds for Owen's Multilinear Extension

Freixas¹

2007

J. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

show abstract

“…Thus, according to the SS preordering, voter i has more a-priori power or control over the collective action of the voting body than the voter j: Sometimes these indices may end up ranking the voters di¤erently (see Saari and Sieberg (2001)). But if we restrict our attention to weighted voting games 1 (see Tomiyama (1987)) or better still swap robust (linear) voting games, which form a larger class of voting games than weighted voting games (see Di¤o Lambo and Moulen (2002)), SS and BC preorderings coincide 2 . Thus, given a simple swap robust game, one way of …nding out the hierarchy induced in the set of players by the decision rule is by evaluating any one of the above mentioned indices for each player.…”

Section: Increased Support For a Bill Cannot Hurt Its Prospectsmentioning

confidence: 99%

Hierarchy of players in swap robust voting games

Bishnu

Roy

2010

Soc Choice Welf

View full text Add to dashboard Cite

Ordinarily, the process of decision making by a committee through voting is modelled by a monotonic game the range of whose characteristic function is restricted to {0,1}. The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori influence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a number-based power index (e.g., the Shapley-Shubik index, the Banzhaf-Coleman index) for each player or conduct a pairwise comparison between players in order to find out whether there exists a coalition in which player i is desirable over another player j as a coalition partner. In this paper we outline a much simpler and more elegant mechanism to determine the ranking of players in terms of their apriori power using only minimal winning coalitions, rather than the entire set of winning coalitions. Abstract Ordinarily, the process of decision making by a committee through voting is modelled by a monotonic game the range of whose characteristic function is restricted to f0; 1g: The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori in ‡uence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a number-based power index (e.g., the Shapley-Shubik index, the Banzhaf-Coleman index) for each player or conduct a pairwise comparison between players in order to …nd out whether there exists a coalition in which player i is desirable over another player j as a coalition partner. In this paper we outline a much simpler and more elegant mechanism to determine the ranking of players in terms of their a-priori power using only minimal winning coalitions, rather than the entire set of winning coalitions.

show abstract

Complete simple games

Cited by 90 publications

References 6 publications

Achievable hierarchies in voting games with abstention

Achievable hierarchies in voting games with abstention

Bounds for Owen's Multilinear Extension

Hierarchy of players in swap robust voting games

Contact Info

Product

Resources

About