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Aggregation and residuation

Author

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  • Bruno Leclerc

    (CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • 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

In this paper, we give a characterization of meet-projections in simple atomistic lattices that generalizes results on the aggregation of partitions in cluster analysis.

Suggested Citation

  • Bruno Leclerc & Bernard Monjardet, 2011. "Aggregation and residuation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00659190, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00659190
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00659190
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    References listed on IDEAS

    as
    1. 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.
    2. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, October.
    3. Dean Neumann & Victor Norton, 1986. "Clustering and isolation in the consensus problem for partitions," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 281-297, September.
    4. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
    5. Monjardet, B., 1990. "Arrowian characterizations of latticial federation consensus functions," Mathematical Social Sciences, Elsevier, vol. 20(1), pages 51-71, August.
    6. Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2007. "Ensembles ordonnés finis : concepts, résultats, usages," Post-Print halshs-00197128, HAL.
    7. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    8. Christopher Chambers & Alan Miller, 2011. "Rules for aggregating information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(1), pages 75-82, January.
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    Cited by:

    1. Chambers, Christopher P. & Miller, Alan D., "undated". "Inefficiency," Working Papers WP2011/14, University of Haifa, Department of Economics, revised 30 Nov 2011.
    2. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    3. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.

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    More about this item

    Keywords

    simple lattice; Aggregation theory; dependence relation; meet-projection; partition; residual map; simple lattice.; Agrégation; application résiduelle; inf-projection; relation de dépendance; treillis simple.;
    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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