On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union

Abstract

We study indirect democracy in which countries, states, or districts each elect a representative who later votes at a union level on their behalf. We show that the voting rule that maximizes the total expected utility of all agents in the union involves assigning a weight to each district's vote and then sticking with the status quo unless at least a threshold of weighted votes is cast for change. We analyze how the weights relate to the population size of a country and the correlation structure of agents' preferences, and then we compare the voting weights in the Council of the European Union under the Nice Treaty and the recently proposed Constitution.

Degressively Proportional Apportionment of Seats in the European Parliament. From a Simple Idea to a Problematic Legal Rule

“…As regards voting on the basis of ideological affinity, the allocation should be proportional to the number of inhabitants. National preferences are best represented by proportionality to the square root of the number of inhabitants, which is connected with their voting power -see inter alia [Barbera, Jackson 2006;Beisbart, Bovens 2007;Moberg 2012]. The family of r-DP methods combines these two cases by the allocation function of the form:…”

Regulation versus taxation

“…If labor and capital taxes are rebated in the same proportion, the majority chooses an environmental tax which is too low. 7 MacKenzie and Onhorf (2012) argue that the distributional conflict is harsher with revenue-rising instruments (e.g. ecotaxes or tradeablepermit auctions) than with non-revenue-raising instruments.…”

“…Also since   ≤  2 , the majority 22 Specifically,  ( *   ) = ( *  • ) and  is defined in Appendix. By (4) and (7), 23  is defined in Appendix. By (7) and (11) 24 Hereafter we assume that Lemma 2 holds.…”

“…By (4) and (7), 23  is defined in Appendix. By (7) and (11) 24 Hereafter we assume that Lemma 2 holds. Cases in which this lemma does not apply are discussed in the Supplementary Material available from the authors upon request.…”

“…The literature on weighted voting is possibly less developed, and mostly concerned with problems of equal representation in indirect democracies Barbera and Jackson (2006). suggest a mixture of weights and super-majority that allows sticking with the status quo, unless at least a threshold of weighted votes is cast for change.…”