scholarly journals An Axiomatization for Two Power Indices for (3,2)-Simple Games

2019 ◽  
pp. 559-582
Author(s):  
Giulia Bernardi ◽  
Josep Freixas
Keyword(s):  
Power Indices ◽  
Simple Games

On Ordinal Equivalence of Power Indices in Simple Games

1987 ◽  
Vol 14 (22) ◽  
pp. 49-60
Author(s):  
Yoshinori Tomiyama
Keyword(s):  
Power Indices ◽  
Simple Games ◽  
Ordinal Equivalence

SOME OPEN PROBLEMS IN SIMPLE GAMES

2013 ◽  
Vol 15 (02) ◽  
pp. 1340005 ◽  
Author(s):  
CESARINO BERTINI ◽  
JOSEP FREIXAS ◽  
GIANFRANCO GAMBARELLI ◽  
IZABELLA STACH
Keyword(s):  
Power Indices ◽  
Review Of Literature ◽  
Simple Games ◽  
Open Problems ◽  
Weighted Games

This paper presents a review of literature on simple games and highlights various open problems concerning such games; in particular, weighted games and power indices.

scholarly journals An issue based power index

2020 ◽  
Author(s):  
Qianqian Kong ◽  
Hans Peters
Keyword(s):  
Linear Order ◽  
Power Index ◽  
Simple Game ◽  
Power Indices ◽  
Weighted Sum ◽  
Simple Games ◽  
Linear Orders ◽  
Transfer Property ◽  
Power Change ◽  
Equal Power

Abstract An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum up to one. We consider a class of power indices, characterized by weight vectors on the set of issues. A power index in this class assigns to each player the weighted sum of the issues for which that player is pivotal. A player is pivotal for an issue if that player is a pivotal player in the coalition consisting of all players preceding that player in the linear order associated with that issue. We present several axiomatic characterizations of this class of power indices. The first characterization is based on two axioms: one says how power depends on the issues under consideration (Issue Dependence), and the other one concerns the consequences, for power, of splitting players into several new players (no advantageous splitting). The second characterization uses a stronger version of Issue Dependence, and an axiom about symmetric players (Invariance with respect to Symmetric Players). The third characterization is based on a variation on the transfer property for values of simple games (Equal Power Change), besides Invariance with respect to Symmetric Players and another version of Issue Dependence. Finally, we discuss how an issue profile may arise from preferences of players about issues.

scholarly journals Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form

2017 ◽  
Vol 26 (6) ◽  
pp. 1231-1245 ◽  
Author(s):  
J. M. Alonso-Meijide ◽  
M. Álvarez-Mozos ◽  
M. G. Fiestras-Janeiro
Keyword(s):  
Partition Function ◽  
Power Indices ◽  
Simple Games ◽  
Function Form ◽  
Partition Function Form ◽  
Minimal Winning Coalitions

SEMIVALUES AND VOTING POWER

2003 ◽  
Vol 05 (01) ◽  
pp. 41-61 ◽  
Author(s):  
ANNICK LARUELLE ◽  
FEDERICO VALENCIANO
Keyword(s):  
Power Indices ◽  
Simple Games ◽  
Voting Power ◽  
The Family ◽  
Voting Procedures

In this paper we revise the axiomatic foundations and meaning of semivalues as measures of power on the domain of simple games, when these are interpreted as models of voting procedures. In this context we characterize the family of preferences on roles in voting procedures they represent, and each of them in particular. To this end we first characterize the family of semivalues and each of them in particular up to the choice of a zero and a unit of scale. As a result a reinterpretation of semivalues as a class of power indices is proposed and critically discussed.

scholarly journals An Axiomatization for Two Power Indices for (3,2)-Simple Games

2019 ◽  
Vol 21 (01) ◽  
pp. 1940001 ◽  
Author(s):  
Giulia Bernardi ◽  
Josep Freixas
Keyword(s):  
Power Index ◽  
Power Indices ◽  
Simple Games ◽  
Banzhaf Index ◽  
Null Player

The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

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