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Consensus theories: an oriented survey

Author

Listed:
  • Olivier Hudry

    (Télécom ParisTech)

  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).

Suggested Citation

  • Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," Post-Print halshs-00504974, HAL.
    • Handle: RePEc:hal:journl:halshs-00504974
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00504974
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    1. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 185-192.
    2. 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, June.
    3. 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.
    4. Maurice Salles, 2016. "Social choice," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 36, pages 518-537, Edward Elgar Publishing.
    5. Ádám Galambos & Victor Reiner, 2008. "Acyclic sets of linear orders via the Bruhat orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 245-264, February.
    6. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    7. Barthelemy, J. P. & Guenoche, A. & Hudry, O., 1989. "Median linear orders: Heuristics and a branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 42(3), pages 313-325, October.
    8. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, September.
    9. Bernard Monjardet & Vololonirina Raderanirina, 2004. "Lattices of choice functions and consensus problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(3), pages 349-382, December.
    10. Barthelemy, Jean-Pierre, 1982. "Arrow's theorem: unusual domains and extended codomains," Mathematical Social Sciences, Elsevier, vol. 3(1), pages 79-89, July.
    11. Olivier Hudry, 2004. "A note on “Banks winners in tournaments are difficult to recognize” by G. J. Woeginger," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 113-114, August.
    12. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, September.
    13. B. Monjardet, 1997. "Concordance between two linear orders: The Spearman and Kendall coefficients revisited," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 269-295, September.
    14. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    15. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    16. Edward Adams, 1986. "N-trees as nestings: Complexity, similarity, and consensus," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 299-317, September.
    17. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    18. Jean-Pierre Barthélemy & Bruno Leclerc & Bernard Monjardet, 1986. "On the use of ordered sets in problems of comparison and consensus of classifications," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 187-224, September.
    19. B. Monjardet, 1978. "An Axiomatic Theory of Tournament Aggregation," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 334-351, November.
    20. Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 523-528, June.
    21. Olivier Hudry, 2008. "NP-hardness results for the aggregation of linear orders into median orders," Annals of Operations Research, Springer, vol. 163(1), pages 63-88, October.
    22. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
    23. Saul Amorim & Jean-Pierre Barthélemy & Celso Ribeiro, 1992. "Clustering and clique partitioning: Simulated annealing and tabu search approaches," Journal of Classification, Springer;The Classification Society, vol. 9(1), pages 17-41, January.
    24. Hudry, Olivier, 2010. "On the complexity of Slater's problems," European Journal of Operational Research, Elsevier, vol. 203(1), pages 216-221, May.
    25. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    26. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
    27. Charon, Irene & Hudry, Olivier, 2001. "The noising methods: A generalization of some metaheuristics," European Journal of Operational Research, Elsevier, vol. 135(1), pages 86-101, November.
    28. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 61-65, March.
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    Cited by:

    1. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2013. "LEVEL r CONSENSUS AND STABLE SOCIAL CHOICE," Working Papers 1305, Ben-Gurion University of the Negev, Department of Economics.
    2. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    3. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.

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    More about this item

    Keywords

    median; tournament solutions; restricted domains; lower valuations; median semilattice; complexity; Consensus theories; Arrowian results; aggregation rules; metric consensus rules; Théories du consensus; résultats arrowiens; règles d'agrégation; distances; médiane; solutions de tournoi; domaines restreints; valuations inférieures; demi-treillis à médianes; complexité;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C0 - Mathematical and Quantitative Methods - - General

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