Condorcet domains, median graphs and the single-crossing property View Full Text


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Article Info

DATE

2019-02

AUTHORS

Clemens Puppe, Arkadii Slinko

ABSTRACT

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it contains the majority relation of every profile with an odd number of voters whose preferences belong to this domain. We show that every closed Condorcet domain can be endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (in general, not uniquely). Condorcet domains that have linear graphs (chains) associated with them are exactly the preference domains with the classical single-crossing property. As a corollary, we obtain that a domain with the so-called ‘representative voter property’ is either a single-crossing domain or a very special domain containing exactly four different preference orders whose associated median graph is a 4-cycle. Maximality of a Condorcet domain imposes additional restrictions on the associated median graph. We prove that among all trees only (some) chains can be associated graphs of maximal Condorcet domains, and we characterize those single-crossing domains which are maximal Condorcet domains. Finally, using the characterization of Nehring and Puppe (J Econ Theory 135:269–305, 2007) of monotone Arrovian aggregation, we show that any closed Condorcet domain admits a rich class of strategy-proof social choice functions. More... »

PAGES

1-34

References to SciGraph publications

  • 1996-12. Acyclic sets of linear orders in SOCIAL CHOICE AND WELFARE
  • 2012-03. Majority relation and median representative ordering in SERIES
  • 1991-12. Representative voter theorems in PUBLIC CHOICE
  • 2009. Acyclic Domains of Linear Orders: A Survey in THE MATHEMATICS OF PREFERENCE, CHOICE AND ORDER
  • 2015-03. Sorting out single-crossing preferences on networks in SOCIAL CHOICE AND WELFARE
  • 2013-03. Maximal Condorcet Domains in ORDER
  • 2008-02. Acyclic sets of linear orders via the Bruhat orders in SOCIAL CHOICE AND WELFARE
  • 2002-04. Acyclic sets of linear orders: A progress report in SOCIAL CHOICE AND WELFARE
  • 1980-01. On strategy-proofness and single peakedness in PUBLIC CHOICE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00199-017-1084-6

    DOI

    http://dx.doi.org/10.1007/s00199-017-1084-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092418565


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