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Aggregation and Residuation

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Abstract

In this note we give a characterization of meet-projections in simple atomistic lattices which generalizes previous results on the aggregation of partitions obtained in a cluster analysis framework.

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References

  1. Arrow, K.J.: Social Choice and Individual Values. Wiley, New York (1951)

    MATH  Google Scholar 

  2. Barthélemy, J.P., Janowitz, M.F.: A formal theory of consensus. SIAM J. Discrete. Math. 4, 305–322 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blyth, T.S., Janowitz, M.F.: Residuation Theory. Pergamon Press, Oxford (1972)

    MATH  Google Scholar 

  4. Brown, D.J.: Aggregation of preferences. Q. J. Econ. 89, 456–469 (1975)

    Article  Google Scholar 

  5. Caspard, N., Leclerc, B., Monjardet, B.: Finite Ordered Sets: Concepts, Results and Uses. Cambridge University Press, Cambridge U.K. (2012)

    MATH  Google Scholar 

  6. Caspard, N., Monjardet, B.: On a dependence relation in finite lattices. Discrete. Math. 165–166, 497–505 (1997)

    MathSciNet  Google Scholar 

  7. Chambers C.P., Miller A.D.: Rules for aggregating information. Soc. Choice Welf. 36(1), 75–82 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  9. Day, A.: Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices. Can. J. Math. 31, 69–78 (1979)

    Article  MATH  Google Scholar 

  10. Day, W.H.E., McMorris, F.R.: Axiomatic Consensus Theory in Group Choice and Biomathematics. SIAM, Philadelphia (2003)

    Book  MATH  Google Scholar 

  11. Dimitrov, D., Marchant, T., Mishra, D.: Separability and aggregation of equivalence relations. Econ. Theory (2011). doi:10.1007/s00199-011-0601-2

  12. Erné, M.: Adjunctions and Galois connections: origins, history and development. In: Denecke, K., Erné, M., Wismath, Sh. (eds.) Galois Connections and Applications, pp. 1–138. Kluwer, Dordrecht (2004)

    Google Scholar 

  13. Freese, R., Jezek, K., Nation, J.B.: Free Lattices. American Mathematical Society, Providence (1995)

    MATH  Google Scholar 

  14. Jonsson, B., Nation, J.B.: A report on sublattices of a free lattice. In: Contributions to Universal Algebra. Coll. Math. Soc. Janos Bolyai, vol. 17, pp. 233–257. North-Holland, Amsterdam (1977)

    Google Scholar 

  15. Leclerc, B.: Efficient and binary consensus functions on transitively valued relations. Math. Soc. Sci. 8, 45–61 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  16. Leclerc, B. Monjardet, B.: Latticial theory of consensus. In: Barnett, V., Moulin, H., Salles, M., Schofield, N. (eds.) Social Choice, Welfare and Ethics, pp. 145–159. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  17. Mirkin, B.G.: On the problem of reconciling partitions. In: Quantitative Sociology, International Perspectives on Mathematical and Statistical Modelling, pp. 441–449. Academic Press, New-York (1975)

    Google Scholar 

  18. Monjardet, B.: Arrowian characterizations of latticial federation consensus functions. Math. Soc. Sci. 20, 51–71 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  19. Neumann, D.A., Norton, Jr, V.T.: Clustering and Isolation in the Consensus Problem for Partitions. J. Classif. 3, 281–297 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Centre d’Analyse et de Mathématique Sociales, École des Hautes Études en Sciences Sociales, 190 avenue de France, 75270, Paris cedex 13, France

    Bruno Leclerc

  2. Centre d’Économie de la Sorbonne, Université Paris I, MSE, 106-112 boulevard de l’Hôpital, 75647, Paris cedex 13, France

    Bernard Monjardet

  3. CAMS, EHESS, Paris, France

    Bernard Monjardet

Authors
  1. Bruno Leclerc
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  2. Bernard Monjardet
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Correspondence to Bernard Monjardet.

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Leclerc, B., Monjardet, B. Aggregation and Residuation. Order 30, 261–268 (2013). https://doi.org/10.1007/s11083-011-9242-0

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  • DOI: https://doi.org/10.1007/s11083-011-9242-0

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