Representation-Compatible Power Indices

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representation-compatible, a property not fulfilled by classical power indices. Average representations can be tailored to reveal the equivalence classes of voters defined by the Isbell desirability relation, which leads to a pair of new power indices that ascribes equal power to all members of an equivalence class.Comment: 28 pages, 1 figure, and 11 table

Weighted Committee Games

Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of different voting weights (share-holdings, party seats, etc.) under plurality, Borda, Copeland, and antiplurality rule. The number and geometry of weight equivalence classes differ widely across the rules. Decisions can be much more sensitive to weights in Borda committees than (anti-)plurality or Copeland ones.Comment: 26 pages, 9 tables, 4 figure

Power distribution in the Basque Parliament using games with externalities

In this paper we study the distribution of power in the Basque Parliament since the restoration of the Spanish democracy. The classic simple games do not fit with the particular voting rule that it is used to invest the president of the regional government. In order to model this voting mechanism we incorporate coalitional externalities to the game. We use the extensions of the most popular power indices to games with externalities that have been proposed in the most recent literature. Moreover, we propose a method to estimate the probability of a given coalition based on the ideological positions of its members in a two-dimensional political spectrum

10101 Abstracts Collection -- Computational Foundations of Social Choice

From March 7 to March 12, 2010, the Dagstuhl Seminar 10101 ``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Equal representation in two-tier voting systems

The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte-Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested

Power indices and minimal winning coalitions for simple games in partition function form

We propose a generalization of simple games to partition function form games based on a monotonicity property that we define in this context. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on such coalitions. Finally, the new indices are used to study the distribution of power in the Parliament of Andalusia that emerged after the elections of March 22, 2015