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Condorcet domains satisfying Arrow’s single-peakedness

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  • Slinko, Arkadii

Abstract

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation of any profile with an odd number of voters is transitive. Maximal Condorcet domains historically have attracted a special attention. We study maximal Condorcet domains that satisfy Arrow’s single-peakedness which is more general than Black’s single-peakedness. We show that all maximal Black’s single-peaked domains on the set of m alternatives are isomorphic but we found a rich variety of maximal Arrow’s single-peaked domains. We discover their recursive structure, prove that all of them have cardinality 2m−1, and characterise them by two conditions: connectedness and minimal richness. We also classify Arrow’s single-peaked Condorcet domains for m≤5 alternatives.

Suggested Citation

  • Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:166-175
    DOI: 10.1016/j.jmateco.2019.08.001
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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. Peter C. Fishburn, 2002. "Acyclic sets of linear orders: A progress report," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 431-447.
    3. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    4. Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Post-Print halshs-00119141, HAL.
    5. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    6. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    7. Peter Fishburn, 1996. "Acyclic sets of linear orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 113-124.
    8. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    9. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    10. Puppe, Clemens & Slinko, Arkadii, 2016. "Condorcet domains, median graphs and the single-crossing property," Working Paper Series in Economics 92, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    11. John Craven, 1996. "Majority-consistent preference orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 259-267.
    12. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 305-322, February.
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