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A Limit Theorem on the Minmax Set

Author

Listed:
  • Gabrielle Demange

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

It is well known that a Condorcet winner may not exist over a multidimensional space. We are concerned in this paper with an extension of the Condorcet's rule: the minmax set. This set, always non-empty, coincides with the set of majority winners whenever they exist. Unfortunately, it may be very large in finite society. We establish that it shrinks to a single point when the population increases smoothly enough under suitable assumptions of single peakedness and intermediate preferences.

Suggested Citation

  • Gabrielle Demange, 1982. "A Limit Theorem on the Minmax Set," Post-Print halshs-00671000, HAL.
    • Handle: RePEc:hal:journl:halshs-00671000
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    Cited by:

    1. Nehring, Klaus & Puppe, Clemens, 2023. "Multi-dimensional social choice under frugal information: The Tukey median as Condorcet winner ex ante by," Working Paper Series in Economics 160, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    3. Nehring, Klaus & Puppe, Clemens, 2022. "Condorcet solutions in frugal models of budget allocation," Working Paper Series in Economics 156, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.

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