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

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Abstract

This paper is dedicated to the measurement of (or lack of) electoral justice in the 2010 Electoral 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 to a 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 probability models which are used and in particular to the type and magnitude of correlation between voters that they carry.

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Notes

Acknowledgements

We are very pleased to offer this paper as a contribution to this volume honoring Bill Gehrlein and Dominique Lepelley with whom we had the pleasure to cooperate in the recent years. Both have made important contributions to the evaluation of voting rules and electoral systems through probability models. Power measurement and two-tier electoral systems, the two topics of our paper, are parts of their general research agenda. We hope that they will find our paper respectful of the approach that they have been promoting in their work. Last, but not least, we would like to thank two anonymous referees who have attracted our attention on the imperfections and shortcomings contained in an earlier version and whose comments and suggestions have improved a lot the exposition of the ideas developed in our paper. Of course, they should not be held responsible for any of the remaining insufficiencies. The working paper version, available on the Web sites of the authors, contains three appendices offering supplementary mathematical developments on the intricacies of the Shapley-Shubik’s probability model and its discrete counterpart. The three first authors acknowledge funding from the French National Research Agency (ANR) under the Investments for the Future program (Investissements d’ Avenir, grant ANR-17 EURE-0010).

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© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Toulouse School of Economics, INRAUniversity of Toulouse CapitoleToulouseFrance
  2. 2.Toulouse School of Economics, CNRSUniversity of Toulouse CapitoleToulouseFrance
  3. 3.Institut Universitaire de France and Toulouse School of EconomicsUniversity of Toulouse CapitoleToulouseFrance
  4. 4.Ecole Normale Supérieure, Department of MathematicsUniversity of Yaounde IYaoundeCameroon

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