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On continuity of Arrovian social welfare functions

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Abstract

We study continuity properties of Arrovian social welfare functions in the infinite population framework. We show that continuous welfare functions satisfying unanimity and independence of irrelevant alternatives are dictatorial. Weak anonymity is shown to be incompatible with continuity and unanimity: every continuous weakly anonymous social welfare function must be a constant function.

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References

  1. Armstrong TE (1980) Arrow's theorem with restricted coalition algebras. J Math Econ 7:55–75

    Article  Google Scholar 

  2. Armstrong TE (1985) Precisely dictatorial social welfare functions. Erratum and addendum to Arrow's theorem with restricted coalition algebras'. J Math Econ 14:57–59

    Article  Google Scholar 

  3. Arrow KJ (1950) A difficulty in the concept of social welfare. J Polit Econ 58:323–328

    Article  Google Scholar 

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

    Google Scholar 

  5. Arrow KJ (1963) Social choice and individual values, 2nd edn. Yale University Press, New Haven

    Google Scholar 

  6. Brown DJ (1974) An approximate solution to Arrow's problem. J Econ Theory 9:375–383

    Article  Google Scholar 

  7. Fishburn PC (1970) Arrow's impossibility theorem: concise proof and infinite voters. J Econ Theory 2:103–106

    Article  Google Scholar 

  8. Hansson B (1976) The existence of group preferences. Public Choice 28:89–98. (Working Paper 1972, Mattias Fremling Society No. 3.)

    Article  Google Scholar 

  9. Kirman AP, Sondermann D (1972) Arrow's theorem, many agents, and invisible dictators. J Econ Theory 5:267–277

    Article  Google Scholar 

  10. McManus M (1982) Some properties of topological social choice functions. Rev Econ Stud 49:447–460

    Article  Google Scholar 

  11. Mihara HR (1997) Arrow's theorem and Turing computability. Econ Theory 10:257–276

    Article  Google Scholar 

  12. Mihara HR (1997) Anonymity and neutrality in Arrow's theorem with restricted coalition algebras. Soc Choice Welf 14:503–512

    Article  Google Scholar 

  13. Murakami Y (1968) Logic and social choice. Routledge and Kegan Paul, London

    Google Scholar 

  14. Schmitz N (1977) A further note on Arrow's impossibility theorem. J Math Econ 4:189–196

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to Prof. M. Salles and an anonymous referee for their valuable comments. I want to thank the Yrjö Jahnsson Foundation for financial support.

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Authors and Affiliations

  1. Department of Economics, University of Turku, 20014, Turku, Finland

    Hannu Salonen

  2. Department of Economics, Turku School of Economics, 20500, Turku, Finland

    Kari Saukkonen

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  1. Hannu Salonen
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  2. Kari Saukkonen
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Correspondence to Hannu Salonen.

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Salonen, H., Saukkonen, K. On continuity of Arrovian social welfare functions. Soc Choice Welfare 25, 85–93 (2005). https://doi.org/10.1007/s00355-005-0030-x

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  • DOI: https://doi.org/10.1007/s00355-005-0030-x

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