Majority Judgment

In the preceding chapters we have seen that the traditional framework for elections, in which voters are supposed to give preference orders over the alternatives, although adopted by almost everyone in the field, is doomed to failure. It was only around 2010 that Balinski and Laraki (Majority Judgment vs Majority Rule. Social Choice and Welfare, 2019. https://doi.org/10.1007/s00355-019-01200-x ) pointed out that Plurality and Majority Rule do not respect dominance, i.e., a candidate with the better evaluations may not become the winner. For that reason they developed a new electoral rule, called Majority Judgment, that takes as input the evaluations of the candidates by the voters instead of their preference orders (or first choice in the case of Plurality Rule). By taking the median value of a candidate’s evaluations, Majority Judgment measures the global support this candidate receives from the electorate. Majority Judgment has many nice properties not shared by other voting systems. Contrary to Plurality Rule and Majority Rule, Majority Judgment is transitive, Independent of Irrelevant Alternatives and respects dominance. In addition, Majority Judgment is strategy-proof with respect to the final judgment (majority grade) of a candidate and partially strategy-proof with respect to the social ranking of the candidates. Balinski and Laraki illustrate their findings with recent presidential elections in the USA and in France, in the meantime pointing out that the French electoral system is not monotonic. They also point out that summing or averaging points is easy to manipulate and not consistent with Majority Judgment nor with Majority Rule, while Approval Voting gives arbitrary outcomes and does not respect dominance. This chapter is an extended version of Harrie de Swart, How to choose a president, mayor, chairman: Balinski and Laraki unpacked, published in The Mathematical Intelligencer 2022, https://doi.org/10.1007/s00283-021-10124-3 ; link to the Creative Common license: https://creativecommons.org/licenses/by/4.0/ . As such it can be read independently of the other chapters. I am grateful to Sergei Tabachnikov (editor) and several anonymous referees for suggesting important improvements.