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Simple Majorities with Voice but No Vote

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Abstract

Oligarchic majority rules bring the voice but no vote principle into effect. We prove characterizations of the oligarchic majority rules for both fixed and unrestricted societies and a binary agenda. This is a general class of rules that includes the simple majority rule as well as dictatorships. Suitable sets of axioms identify a subsociety whose members have voice but no vote, and valid votes are aggregated by the majority rule.

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Notes

  1. Woeginger (2005) refers to biased voters. Still other authors write concerned voters instead.

  2. If no confusion is possible, we simply drop the reference to the social welfare function F and say that the profile is irrelevant-free.

  3. Another counterexample is the “unanimity” rule that declares \(F(R)=0\) when \(R\ne (1, \ldots , 1)\) and \(R\ne (-1, \ldots , -1)\); \(F(1, \ldots , 1)=1\); and \(F(-1, \ldots , -1) = -1\). Observe that when \(n=2\), \(F(1,1)\ne F(F(1,0), F(0,1))\) therefore RI is not satisfied.

  4. Weymark (2014a, b) are nice introductions to the history of Allan Gibbard’s seminar notes (Gibbard 2014a) and unpublished paper (Gibbard 2014b).

  5. Miroiu (2013) gives an exhaustive analysis of responsiveness properties (like AR and PR) which can be used to prove similar characterizations of the majority rule.

  6. The reader may consult Bartholdi et al. (2019) and Isaacs (2008) for the definitions from group theory.

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Acknowledgements

The author is grateful to the Coordinating Editor and two anonymous reviewers for their very valuable comments, which improved the quality of the paper. The author thanks audiences of the ASSET 2018 conference in Firenze, and seminar presentations in Valladolid and Catania.

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  1. BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007, Salamanca, Spain

    José Carlos R. Alcantud

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  1. José Carlos R. Alcantud
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Correspondence to José Carlos R. Alcantud.

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Alcantud, J.C.R. Simple Majorities with Voice but No Vote. Group Decis Negot 29, 803–822 (2020). https://doi.org/10.1007/s10726-020-09663-5

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