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Quota Manipulation And Fair Voting Rules In Committees

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  • Frantisek Turnovec

Abstract

The concept of fair representation of voters in a committee representing different groups of voters, such as national representations in union of states, is discussed. This concept, introduced into discussion about voting rights in the Council of European Union in 2004, was narrowed to a proposal of distribution of voting weights among the member states proportionally to square roots of population. Such a distribution should guarantee the same indirect voting power to each EU citizen, measured by Penrose-Banzhaf index of voting power. In this paper we analyze problem of fairness in committee voting in a more general framework: assuming that distribution of voting weights in a simple voting committee is fair (whatever does it mean), how to set up voting rule to guarantee that distribution of influence (relative voting power) is as close as possible to relative voting weights. Model of simple weighted committee is used, defined as a pair [N, w], where N be a finite set of n committee members , and w = (w1, w2, …, wn) be a nonnegative vector of committee members’ voting weights (e.g. votes or shares). By voting coalition we mean a subset S of N of committee members voting uniformly (YES or NO). The voting rule is defined by quota q representing the minimal total weight necessary to approve the proposal. A coalition S is winning if its total weight is not less than quota. A priori voting power analysis seeks an answer to the following question: Given a simple weighted committee and a quota, what is an influence of its members over the outcome of voting? The absolute voting power of a member i is defined as a probability pi(N, q, w) that i will be decisive in the sense that such a situation appears in which she would be able to decide the outcome of voting by her vote. In a committee with fixed number of members and fixed weights the a priori voting power is a function of quota q. Explicit representation of this function is studied. In simple weighted committees with a finite number n of members, fixed weights and changing quota, there exists a finite number of different quota intervals of stable power (generating finite number of different voting rules) with the same sets of winning coalitions for all quotas from each of them. If the fair distribution of voting weights is defined, then the fair distribution of voting power means to find a quota that minimizes the distance between relative voting weights and relative voting power (fair quota). The problem of the fair quota has an exact solution via the finite number of quotas from different intervals of stable power.

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  • Frantisek Turnovec, 2011. "Quota Manipulation And Fair Voting Rules In Committees," EcoMod2011 3186, EcoMod.
    • Handle: RePEc:ekd:002625:3186
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