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Proximity by Numbers

Author

Listed:
  • Conal Duddy
  • Ashley Piggins

    (Department of Economics, National University of Ireland, Galway)

Abstract

Imagine that everyone in a group chooses a real number and then these numbers are combined to produce a group number. Suppose that when everyone moves strictly closer to some individual’s number, the group number either stays where it is or moves closer to this number. We call this the proximity condition. Restricting attention to group choice rules that are homogeneous of degree one and constant-preserving, we show that the only rules satisfying this property are dictatorships.

Suggested Citation

  • Conal Duddy & Ashley Piggins, 2009. "Proximity by Numbers," Working Papers 0155, National University of Ireland Galway, Department of Economics, revised 2009.
  • Handle: RePEc:nig:wpaper:0155
    as

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    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=162
    File Function: First version, 2009
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    File URL: http://www.economics.nuig.ie/resrch/paper.php?pid=162
    File Function: Revised version, 2009
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    References listed on IDEAS

    as
    1. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    2. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    3. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 305-318.
    4. Asley Piggins & Maurice Salles, 2007. "Instances of Indeterminacy," Post-Print halshs-00337772, HAL.
    5. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
    6. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    7. Perote-Pena, Juan & Piggins, Ashley, 2007. "Strategy-proof fuzzy aggregation rules," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 564-580, June.
    8. Barrett, C.R. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Institut des Mathématiques Economiques – Document de travail de l’I.M.E. (1974-1993) 9006, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
    9. Dutta, Bhaskar & Panda, Santosh C. & Pattanaik, Prasanta K., 1986. "Exact choice and fuzzy preferences," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 53-68, February.
    10. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
    11. Maurice Salles, 2005. "Social Choice," Post-Print halshs-00337075, HAL.
    12. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2010. "Manipulating an aggregation rule under ordinally fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 411-428, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Proximity condition; merging function; impossibility theorem Algorithmic Trading; MACD;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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