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.
Highlights
1.1 BackgroundPower indices for simple games measure the power of players in such a game, independently of the issues at stake or the positions of players regarding these issues
In the second characterization (Theorem 4.1) we consider the axiom of Invariance with respect to Symmetric Players: given any issue game and two players i and i who are symmetric in the associated simple game, if i is pivotal for an issue and we change the linear order of that issue so that i becomes pivotal, the power assigned to every other player should not change
We identify the universe of potential players with N
Summary
Power indices for simple games measure the power of players in such a game, independently of the issues at stake or the positions of players regarding these issues. For a relatively recent overview of power indices for simple games see Bertini et al (2013) These power indices include the Shapley value (Shapley 1953), called Shapley–Shubik index (Shapley and Shubik 1954), the Banzhaf value (Banzhaf 1965; Shenoy 1982; Nowak 1997) and the Banzhaf–Coleman index (Coleman 1971), the Holler index (Holler 1982), and many more. Most of these power indices, including the ones mentioned, are based on counting in some way or another the number of times a player is pivotal in the simple game. Still other approaches model the impact of preferences on power by means of a noncooperative voting game: see, for instance, Schmidtchen and Steunenberg (2014)
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call