Implications of Voter Interaction on the Optimal Weights within Heterogeneous Voting Systems

Abstract

This article examines the implications of various voter interaction hypotheses within the collective bias model on the fair weights in heterogeneous voting systems. In such systems, political decision-making is carried out by member state representatives that are assigned individual weights in order to ensure an appropriate representation. Yet the optimal weights vary in terms of different hypotheses of voter interaction in each member state. In particular, this paper analyses the cases in which voters are independent from each other, in which they interact only at the national level, and in which they are homogeneously correlated throughout the entire federation of states, respectively.For independent voting, the optimal weights are supposed to be proportional to the square-root of the population size. Interaction (only) within member states is associated with a power law, which varies from the square-root to linearity of the populations in parallel with the degree of homogeneity among each of them. For transnational interaction, optimal weights are ambiguous, as for sufficiently large populations any distribution of weights is shown to be optimal.