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Oligarchy and soft incompleteness

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  • Piggins, Ashley
  • Duddy, Conal

Abstract

The assumption that the social preference relation is complete is demanding. We distinguish between “hard” and “soft” incompleteness, and explore the social choice implications of the latter. Under soft incompleteness, social preferences can take values in the unit interval. We motivate interest in soft incompleteness by presenting a version of the strong Pareto rule that is suited to the context of a [0, 1]-valued social preference relation. Using a novel approach to the quasi-transitivity of this relation we prove a general oligarchy theorem. Our framework allows us to make a distinction between a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be undesirable.

Suggested Citation

  • Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:72392
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    File URL: https://mpra.ub.uni-muenchen.de/72392/1/MPRA_paper_72392.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Oligarchy; Gibbard’s theorem; Incompleteness; Max-star transitivity;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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