View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Liverpool Repository Majority Judgment vs. Majority Rule ∗ Michel Balinski CNRS, CREST, Ecole´ Polytechnique, France,
[email protected] and Rida Laraki* CNRS, University of Paris Dauphine-PSL, France,
[email protected] and University of Liverpool, United Kingdom June 6, 2019 Abstract The validity of majority rule in an election with but two candidates|and so also of Condorcet consistency| is challenged. Axioms based on evaluating candidates|paralleling those of K. O. May characterizing ma- jority rule for two candidates based on comparing candidates|lead to another method, majority judgment, that is unique in agreeing with the majority rule on pairs of \polarized" candidates. It is a practical method that accommodates any number of candidates, avoids both the Condorcet and Arrow paradoxes, and best resists strategic manipulation. Key words: majority, measuring, ranking, electing, Condorcet consistency, domination paradox, tyranny of majority, intensity problem, majority-gauge, strategy-proofness, polarization. 1 Introduction Elections measure. Voters express themselves, a rule amalgamates them, the candidates' scores|measures of support|determine their order of finish, and the winner. Traditional methods ask voters to express themselves by comparing them: • ticking one candidate at most (majority rule, first-past-the-post) or several candidates (approval voting), candidates' total ticks ranking them; • rank-ordering the candidates (Borda rule, alternative vote or preferential voting, Llull's rule, Dasgupta- Maskin method, . ), differently derived numerical scores ranking them. However, no traditional method measures the support of one candidate.1 Instead, the theory of voting (or of social choice) elevates to a basic distinguishing axiom the faith that in an election between two candidates majority rule is the only proper rule.