Skip to main content
SpringerLink
Log in

Manipulating an aggregation rule under ordinally fuzzy preferences

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

It is well known that many aggregation rules are manipulable through strategic behaviour. Typically, the aggregation rules considered in the literature are social choice correspondences. In this paper the aggregation rules of interest are social welfare functions (SWFs). We investigate the problem of constructing a SWF that is non-manipulable. In this context, individuals attempt to manipulate a social ordering as opposed to a social choice. Using techniques from an ordinal version of fuzzy set theory, we introduce a class of ordinally fuzzy binary relations of which exact binary relations are a special case. Operating within this family enables us to prove an impossibility theorem. This theorem states that all non-manipulable SWFs are dictatorial, provided that they are not constant. This theorem uses a weaker transitivity condition than the one in Perote-Peña and Piggins (J Math Econ 43:564–580, 2007), and the ordinal framework we employ is more general than the cardinal setting used there. We conclude by considering several ways of circumventing this impossibility theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abdelaziz FB, Figueira JR, Meddeb O (2008) On the manipulability of the fuzzy social choice functions. Fuzzy Sets Syst 159: 177–184

    Article  Google Scholar 

  • Arrow KJ (1951) Social choice and individual values. Wiley, New York

    Google Scholar 

  • Banerjee A (1994) Fuzzy preferences and Arrow-type problems in social choice. Soc Choice Welf 11: 121–130

    Article  Google Scholar 

  • Barberá S (2001) An introduction to strategy-proof social choice functions. Soc Choice Welf 18: 619–653

    Article  Google Scholar 

  • Barrett CR, Pattanaik PK (1989) Fuzzy sets, preference and choice: some conceptual issues. Bull Econ Res 41: 229–253

    Article  Google Scholar 

  • Barrett CR, Pattanaik PK, Salles M (1986) On the structure of fuzzy social welfare functions. Fuzzy Sets Syst 19: 1–10

    Article  Google Scholar 

  • Barrett CR, Pattanaik PK, Salles M (1992) Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets Syst 49: 9–13

    Article  Google Scholar 

  • Basu K, Deb R, Pattanaik PK (1992) Soft sets: an ordinal reformulation of vagueness with some applications to the theory of choice. Fuzzy Sets Syst 45: 45–58

    Article  Google Scholar 

  • Billot A (1995) Economic theory of fuzzy equilibria. Springer, Berlin

    Google Scholar 

  • Bossert W, Storcken T (1992) Strategy-proofness of social welfare functions: the use of the Kemeny distance between preference orderings. Soc Choice Welf 9: 345–360

    Article  Google Scholar 

  • Broome J (1997) Is incommensurability vagueness. In: Chang R Incommensurability, incomparability, and practical reason. Harvard University Press, Harvard

  • Côrte-Real PP (2007) Fuzzy voters, crisp votes. Int Game Theory Rev 9: 67–86

    Article  Google Scholar 

  • Dasgupta M, Deb R (1996) Transitivity and fuzzy preferences. Soc Choice Welf 13: 305–318

    Article  Google Scholar 

  • Dasgupta M, Deb R (1999) An impossibility theorem with fuzzy preferences. In: de Swart H (ed) Logic, game theory and social choice: proceedings of the international conference. LGS ’99, May 13–16. Tilburg University Press, Tilburg

  • Dasgupta M, Deb R (2001) Factoring fuzzy transitivity. Fuzzy Sets Syst 118: 489–502

    Article  Google Scholar 

  • Dutta B (1987) Fuzzy preferences and social choice. Math Soc Sci 13: 215–229

    Article  Google Scholar 

  • Fono LA, Andjiga NG (2005) Fuzzy strict preference and social choice. Fuzzy Sets Syst 155: 372–389

    Article  Google Scholar 

  • Fishburn PC (1970) Comments on Hansson’s “Group preferences”. Econometrica 38: 933–935

    Article  Google Scholar 

  • Gaertner W (2006) A primer in social choice theory. Oxford University Press, Oxford

    Google Scholar 

  • Gibbard AF (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–601

    Article  Google Scholar 

  • Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18: 145–174

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Leclerc B (1991) Aggregation of fuzzy preferences: a theoretic Arrow-like approach. Fuzzy Sets Syst 43: 291–309

    Article  Google Scholar 

  • Leclerc B, Monjardet B (1995) Lattical theory of consensus. In: Barnett W, Moulin H, Salles M, Schofield N Social choice, welfare and ethics. Cambridge University Press, Cambridge

  • Ovchinnikov SV (1991) Social choice and Lukasiewicz logic. Fuzzy Sets Syst 43: 275–289

    Article  Google Scholar 

  • Pattanaik PK (1973) On the stability of sincere voting situations. J Econ Theory 6: 558–574

    Article  Google Scholar 

  • Perote-Peña J, Piggins A (2007) Strategy-proof fuzzy aggregation rules. J Math Econ 43: 564–580

    Article  Google Scholar 

  • Perote-Peña J, Piggins A (2009a) Non-manipulable social welfare functions when preferences are fuzzy. J Logic Comput 19: 503–515

    Article  Google Scholar 

  • Perote-Peña J, Piggins A (2009b) Social choice, fuzzy preferences and manipulation. In: Boylan T, Gekker R Economics, rational choice and normative philosophy. Routledge, London

  • Piggins A, Salles M (2007) Instances of indeterminacy. Anal Kritik 29: 311–328

    Google Scholar 

  • Richardson G (1998) The structure of fuzzy preferences: social choice implications. Soc Choice Welf 15: 359–369

    Article  Google Scholar 

  • Salles M (1998) Fuzzy utility. In: Barbera S, Hammond PJ, Seidl C Handbook of utility theory, vol 1: principles. Kluwer, Dordrecht

  • Satterthwaite M (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–217

    Article  Google Scholar 

  • Sen AK (1970a) Interpersonal aggregation and partial comparability. Econometrica 38: 393–409

    Article  Google Scholar 

  • Sen AK (1970b) Collective choice and social welfare. Holden-Day, San Francisco

    Google Scholar 

  • Tang F-F (1994) Fuzzy preferences and social choice. Bull Econ Res 46: 263–269

    Article  Google Scholar 

  • Taylor AD (2005) Social choice and the mathematics of manipulation. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Williamson T (1994) Vagueness. Routledge, London

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. J.E. Cairnes School of Business and Economics, National University of Ireland, Galway, University Road, Galway, Ireland

    Conal Duddy & Ashley Piggins

  2. Departamento de Análisis Económico, Universidad de Zaragoza, Gran Vía 2, 50005, Zaragoza, Spain

    Juan Perote-Peña

Authors
  1. Conal Duddy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Perote-Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashley Piggins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashley Piggins.

Additional information

We are grateful to seminar participants at NUI Galway, King’s College London, Universität Osnabrück, Queen’s University Belfast and PET 08 for comments and suggestions. In addition, we would like to thank Nick Baigent, James Jordan, Christian List, Andrew McLennan, Vincent Merlin, Maurice Salles and two anonymous referees for a number of helpful remarks. Financial support from the Spanish Ministry of Science and Innovation through Feder grant SEJ2007-67580-C02-02, the NUI Galway Millennium Fund and the Irish Research Council for the Humanities and Social Sciences is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Duddy, C., Perote-Peña, J. & Piggins, A. Manipulating an aggregation rule under ordinally fuzzy preferences. Soc Choice Welf 34, 411–428 (2010). https://doi.org/10.1007/s00355-009-0405-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-009-0405-5

Keywords

Search

Navigation