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

Are weighted games sufficiently good for binary voting?

Binary yes-no decisions in a legislative committee or a shareholder meeting are commonly modeled as a weighted game. However, there are noteworthy exceptions. E.g., the voting rules of the European Council according to the Treaty of Lisbon use a more complicated construction. Here we want to study the question if we lose much from a practical point of view, if we restrict ourselves to weighted games. To this end, we invoke power indices that measure the influence of a member in binary decision committees. More precisely, we compare the achievable power distributions of weighted games with those from a reasonable superset of weighted games. It turns out that the deviation is relatively small.Comment: 7 pages, 2 tables; typos correcte

Meaningful Learning in Weighted Voting Games: An Experiment

International audienceBy employing binary committee choice problems, this paper investigates how varying or eliminating feedback about payoffs affects: (1) subjects' learning about the underlying relationship between their nominal voting weights and their expected payoffs in weighted voting games; and (2) the transfer of acquired learning from one committee choice problem to a similar but different problem. In the experiment, subjects choose to join one of two committees (weighted voting games) and obtain a payoff stochastically determined by a voting theory. We found that: (i) subjects learned to choose the committee that generates a higher expected payoff even without feedback about the payoffs they received; and (ii) there was statistically significant evidence of ``meaningful learning'' (transfer of learning) only for the treatment with no payoff-related feedback. This finding calls for re-thinking existing models of learning to incorporate some type of introspection

Achievable hierarchies in voting games with abstention

It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley-Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of influence relation. (C) 2013 Elsevier B.V. All rights reserved.Peer ReviewedPostprint (author’s final draft

Ready for the design of voting rules?

The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and conjectures.Comment: 10 page

Bounds for the Nakamura number

The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has also been characterized. However, in general, not much is known about lower and upper bounds depending of invariants on simple, complete or weighted games. Here, we survey such results and highlight connections with other game theoretic concepts.Comment: 23 pages, 3 tables; a few more references adde