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On Top-connected Single-peaked and Partially Single-peaked Domains

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  • Achuthankutty, Gopakumar
  • Roy, Souvik

Abstract

We characterize all domains for which the set of unanimous and strategy-proof social choice functions coincides with the set of min-max rules. As an application of our result, we obtain a characterization of unanimous and strategy-proof social choice functions on maximal single-peaked domains (Moulin (1980), Weymark (2011)), minimally rich single-peaked domains (Peters et al. (2014)), maximal regular single-crossing domain (Saporiti (2009)), and distance based single-peaked domains. We further consider domains that exhibit single-peaked property only over a subset of alternatives. We call such domains top-connected partially single-peaked domains. We characterize the unanimous and strategy-proof social choice function on such domains. As an application of this result, we obtain a characterization of the unanimous and strategy-proof social choice functions on multiple single-peaked domains (Reffgen (2015)), single-peaked domains on graphs, and several other domains of practical significance.

Suggested Citation

  • Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:78102
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    References listed on IDEAS

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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