Voting and Collective Decision-Making

Abstract

Every day thousands of decisions are made by all kinds of committees, parliaments, councils and boards by a 'yes–no' voting process. Sometimes a committee can only accept or reject the proposals submitted to it for a decision. On other occasions, committee members have the possibility of modifying the proposal and bargaining an agreement prior to the vote. In either case, what rule should be used if each member acts on behalf of a different-sized group? It seems intuitively clear that if the groups are of different sizes then a symmetric rule (e.g. the simple majority or unanimity) is not suitable. The question then arises of what voting rule should be used. Voting and Collective Decision-Making addresses this and other issues through a study of the theory of bargaining and voting power, showing how it applies to real decision-making contexts.

An axiomatic characterization of the potential decisiveness index

“…For instance, either the Banzhaf or the two Coleman's power indices admit several axiomatic characterizations but also a probabilistic interpretation, see e.g. [27]. We also refer the interested reader to [22] and [23] for additional theoretical information about Ω, which, as far as we know, is the only tool expressly introduced to measure the potential decisiveness of voters in the context of assessed simple games.…”

On Public Values and Power Indices

“…Then, König and Bräuninger in (1998) reinvented it. In the literature, this index is also called the inclusiveness index, and it can been seen as a measure of success (see, for example, Laruelle, Valenciano, 2011). The König and Bräuninger index, KB, of a simple game W for a player i is defined by:…”

Success and decisiveness on proper symmetric games

“…But only a few authors before A. Laruelle and F. Valenciano had referred to the idea of success (the likelihood of obtaining the result that one votes for) as being also a relevant point to take into account when measuring voting power (see [2], [3], [4], [12], [21], [19]). The sound and lucid analysis made by Laruelle and Valenciano about these concepts in [14], [13] and [15] lead us to work on the cases described in this paper. Being more specific, they proved in [13] that success and decisiveness are in general not only conceptually different but also analytically independent, and they showed in [15] (Example 3.1) that two symmetric games can be differently ranked from these two points of view.…”

“…The sound and lucid analysis made by Laruelle and Valenciano about these concepts in [14], [13] and [15] lead us to work on the cases described in this paper. Being more specific, they proved in [13] that success and decisiveness are in general not only conceptually different but also analytically independent, and they showed in [15] (Example 3.1) that two symmetric games can be differently ranked from these two points of view.…”