The power index at infinity: Weighted voting in sequential infinite anonymous games

Abstract

After we describe the waiting queue problem, we identify a partially observable 2n+1-player voting game with only one pivotal player; the player at the n-1 order. Given the simplest rule of heterogeneity presented in this paper, we show that for any infinite sequential voting game of size 2n+1, a power index of size n is a good approximation of the power index at infinity, and it is difficult to achieve. Moreover, we show that the collective utility value of a coalition for a partially observable anonymous game given an equal distribution of weights is n²+n. This formula is developed for infinite sequential anonymous games using a stochastic process that yields a utility function in terms of the probability of the sequence and voting outcome of the coalition. Evidence from Wikidata editing sequences is presented and the results are compared for 10 coalitions.