Absract:

We consider a two-stage probabilistic model of weighted voting and provide a necessary and sufficient condition under which any symmetric rule is more likely to favor the minority than the proportional rule. We show that the most critical factor is the ratio of the expected variance of the group margin to the variance of the expected group margin. The mathematical condition is interpreted, using concepts such as noisiness, wasted votes and statistical gerrymandering. A series of examples illustrate that the winner-take-all rule is likely to favor the minority under fairly general conditions, while there is one class of preference distributions with which the winner-take-all rule is less likely to favor the minority: a polarized society. The model is extended to endogenous voting, in which we show that minority favoring of the winner-take-all rule is reinforced by the underdog effect. Our numerical computation verifies the sensibility of the asymptotic analysis.

Joint with Zijun Wang

Location:

Room 2E29, CEPS ENS Paris-Saclay
4 avenue des Sciences, 91190, Gif-sur-Yvette