Arguing for Majority Rule* (original) (raw)
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MAJORITY RULE, 2019
May's theorem: mathematically proving that simple majority voting is the only anonymous, neutral, and positively responsive social choice function between two alternatives. That is, it's the only rule that meets those three categories.
K. May characterized majority rule as a function satisfying anonymity, neutrality, and responsiveness. Recent work criticized his characterization and opened the way to the introduction of properties defined by taking into account an entire set of societies. Following this approach, this paper presents a new axiomatization of majority rule that appeals, besides a variant of May's responsiveness, to new properties I will call bnull societyQ and bsubsets decomposabilityQ. D
International Economic Review
May's theorem (1952) shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of "independence of irrelevant alternatives" for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.
Majority rule in the absence of a majority
What is the meaning of "majoritarianism" as a principle of democratic group decision-making in a judgement aggregation problem, when the propositionwise majority view is logically inconsistent? We argue that the majoritarian ideal is best embodied by the principle of supermajority efficiency (SME). SME reflects the idea that smaller supermajorities must yield to larger supermajorities. We show that in a well-demarcated class of judgement spaces, the SME outcome is generically unique. But in most spaces, it is not unique; we must make trade-offs between the different supermajorities. We axiomatically characterize the class of additive majority rules, which specify how such trade-offs are made. This requires, in general, a hyperrealvalued representation.
On the Philosophy of Group Decision Methods I: The Nonobviousness of Majority Rule
Philosophy Compass, 2009
Majority rule is often adopted almost by default as a group decision rule. One might think, therefore, that the conditions under which it applies, and the argument on its behalf, are well understood. However, the standard arguments in support of majority rule display systematic deficiencies. This article explores these weaknesses, and assesses what can be said on behalf of majority rule.
2018
A collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative ’x’, is in the set selected by a collective choice rule for some collective choice problem. Now suppose that ‘x’ rises above another selected alternative ‘y’ in some individual’s preferences. If the collective choice rule is “positively responsive”, ‘x’ remains selected but ‘y’ is no longer selected. If the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule (May 1952). If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash’s version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. Further, ...
Majority judgment vs. majority rule
Social Choice and Welfare, 2019
The validity of majority rule in an election with but two candidates-and so also of Condorcet consistency-is challenged. Axioms based on evaluating candidatesparalleling those of K. O. May characterizing majority 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.
On the Philosophy of Group Decision Methods II: Alternatives to Majority Rule
Philosophy Compass, 2009
In this companion piece to 'On the Philosophy of Group Decision Methods I: The Non-Obviousness of Majority Rule', we take a closer look at some competitors of majority rule. This exploration supplements the conclusions of the other piece, as well as offers a furtherreaching introduction to some of the challenges that this field currently poses to philosophers.