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...

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...

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 develop a theoretical framework for equity in council voting games (CVGs). In a CVG, a fully representative voting body delegates decision-making to a subset of the members, as describes, e.g., the United Nations Security Council (UNSC). Three equity concepts are proposed: ex-ante...

This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not. --...

We consider a committee that consists of n members with one person one vote approving a proposal if the number of affirmative votes from the members reaches threshold k. Which threshold k between 1 and n is "good" for the committee? We suppose that if a new threshold k' proposed by some...

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 consider a dynamic process of collective choice under majority rule in which a status quo policy evolves. The analysis is based on stochastic evolutionary game theory. The Condorcet winner is uniquely a long-run equilibrium for all (super-)majority rules. When the Condorcet winner does not...

Twenty years of negotiations over reform of the United Nations Security Council (UNSC) are yet to bear fruit. We use recent advances in the theory of a-priori voting power to present a formal quantitative appraisal of the "structural reforms" contained within eleven current reform proposals, and...

A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of...