Theory and Decision 84 (4):525-546 (2018)

Abstract
Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of the election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states.
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DOI 10.1007/s11238-018-9660-1
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Statistical Inference.G. Casella & R. L. Berger - 2002 - Thomson Learning.

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