“One Man One Vote”. Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May

Abstract

This paper is dedicated to the measurement of (or lack of) electoral justice in the 2010Electoral College using a methodology based on the expected influence of the vote of each citizen for three probability models. Our first contribution is to revisit and reproduce the results obtained by Owen (1975) for the 1960 and 1970 Electoral College. His work displays an intriguing coincidence between the conclusions drawn respectively from the Banzhaf and Shapley-Shubik’s probability models. Both probability models conclude toa violation of electoral justice at the expense of small states. Our second contribution is to demonstrate that this conclusion is completely flipped upside-down when we use May’s probability model: this model leads instead to a violation of electoral justice at the expense of large states. Besides unifying disparate approaches through a common measurement methodology, one main lesson of the paper is that the conclusions are sensitive to the prob-ability models which are used and in particular to the type and magnitude of correlation between voters that they carry.

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Reference

Olivier de Mouzon, Thibault Laurent, Michel Le Breton, and Issofa Moyouwou, ““One Man One Vote”. Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May”, in Evaluating Voting Systems with Probability Models, Mostopha Diss, and Vincent Merlin (eds.), January 2021, Springer Verlag.