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Single-peaked Compatible Preference Profiles: Some Combinatorial Results

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Abstract

This paper examines combinatorial problems in connection with single-peaked preference orderings on a unidimensional scale. A binary relation, dominance, is defined on the set of connected orderings. Relevant properties of the corresponding poset and cover graph are discussed. A formula for the number of pairs of connected orderings consistent with spatial single-peakedness is derived. The total number of such pairs is shown to be expressible in a simple form involving binomial probabilities. A possible application is a coalition formation process of the kind examined by Brams et al. (J Theor Polit 14:359–383, 2002), where actors have single-peaked preferences on a common scale.

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References

  • Axelrod R (1970) Conflict of interest. A theory of divergent goals with applications to politics. Markham, Chicago

    Google Scholar 

  • Bilbao JM, Jimenez A, Lopez JJ (1998) The Banzhaf power index on convex geometries. Math Soc Sci 35:157–173

    Article  Google Scholar 

  • Black D (1958) Theory of committees and elections. Cambridge University Press, Cambridge

    Google Scholar 

  • Bogart KP (2000) Introductory Combinatorics, 3rd edn. Harcourt Academic Press, San Diego

    Google Scholar 

  • Brams SJ, Jones MA, Kilgour DM (2002) The paradox of disconnected coalitions. J Theor Polit 14:359–383

    Article  Google Scholar 

  • Coombs CH (1964) A theory of data. Wiley, New York

    Google Scholar 

  • Craven J (1992) Social Choice. Cambridge University Press, Cambridge

    Google Scholar 

  • Edelman P (1997) A note on voting. Math Soc Sci 34:37–50

    Article  Google Scholar 

  • Edelman P, Jamison R (1985) The theory of convex geometries. Dedicata 19:247–270

    Google Scholar 

  • Fishburn P (1974) The theory of social choice. Princeton University Press, Princeton

    Google Scholar 

  • Perlinger T (2000) Voting power in an ideological spectrum – The Markov-Pólya index. Math Soc Sci 40:215–226

    Article  Google Scholar 

  • Perlinger T (2001) A note on voting games and ideological compatibility. Statistics Department, University of Lund, Mimeo

    Google Scholar 

  • Roberts FS (1976) Discrete mathematical models. Prentice Hall, New Jersey

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Lund, Box 743, 220 07, Lund, Sweden

    Sven Berg

  2. Baltic Business School, Kalmar University, 391 82, Kalmar, Sweden

    Thommy Perlinger

Authors
  1. Sven Berg
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  2. Thommy Perlinger
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Correspondence to Sven Berg.

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Berg, S., Perlinger, T. Single-peaked Compatible Preference Profiles: Some Combinatorial Results. Soc Choice Welfare 27, 89–102 (2006). https://doi.org/10.1007/s00355-006-0115-1

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  • DOI: https://doi.org/10.1007/s00355-006-0115-1

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