Power indices have been used to evaluate the allocation of power in a wide range of voting situations. While they use the language of game theory known measures of a priori voting power are hardly more than statistical expectations assuming the random behaviour of the players. We introduce a...

Approval voting allows voters to list any number of candidates. Their scores are obtained by summing the votes cast in their favor. Fractional voting instead follows the One-person-one-vote principle by endowing voters with a single vote that they may freely distribute among candidates. In this...

We investigate the method of power indices to study voting power of members of a legislature that has voting blocs. Our analysis is theoretical, intended to contribute to a theory of positive political science in which social actors are motivated by the pursuit of power as measured by objective...

We provide a new proof of the non-emptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their "balanced cover games", which are non-empty, can be...

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and...

A simple game (N,v) is given by a set N of n players and a partition of 2N into a set L of losing coalitions L with value v(L) = 0 that is closed under taking subsets and a set W of winning coalitions W with v(W) = 1. Simple games with α = minp>0 maxW∈W,L∈L p(L) p(W) < 1 are exactly the weighted voting games. We show that α 6 1 4n for every simple game (N,v), confi rming the conjecture of Freixas and Kurz (IJGT, 2014). For complete simple games, Freixas and Kurz conjectured that α = O(√n). We prove this conjecture up to a ln n factor. We also prove that for graphic simple games, that is, simple games in which every minimal winning coalition has size 2, computing α is NP-hard, but polynomial-time solvable if the underlying graph is bipartite. Moreover, we show that for every graphic simple game, deciding if α < a is polynomial-time solvable for every fixed a > 0

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous...

We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said...

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be...