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On continuity of incomplete preferences

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  • Georgios Gerasimou

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Abstract

A weak (strict) preference relation is continuous if it has a closed (open) graph; it is hemicontinuous if its upper and lower contour sets are closed (open). If preferences are complete these four conditions are equivalent. Without completeness continuity in each case is stronger than hemicontinuity. This paper provides general characterizations of continuity in terms of hemicontinuity for weak preferences that are modeled as (possibly incomplete) preorders and for strict preferences that are modeled as strict partial orders. Some behavioral implications associated with the two approaches are also discussed. Copyright Springer-Verlag 2013

Suggested Citation

  • Georgios Gerasimou, 2013. "On continuity of incomplete preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 157-167, June.
  • Handle: RePEc:spr:sochwe:v:41:y:2013:i:1:p:157-167
    DOI: 10.1007/s00355-012-0673-3
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    References listed on IDEAS

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    1. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    2. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    3. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    4. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    5. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    6. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
    7. Paola Manzini & Marco Mariotti, 2008. "On the Representation of Incomplete Preferences Over Risky Alternatives," Theory and Decision, Springer, vol. 65(4), pages 303-323, December.
    8. Bergstrom, Theodore C. & Parks, Robert P. & Rader, Trout, 1976. "Preferences which have open graphs," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 265-268, December.
    9. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    10. Jack Stecher, 2008. "Existence of approximate social welfare," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 43-56, January.
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    Cited by:

    1. Marc Fleurbaey & Erik Schokkaert, 2013. "Behavioral Welfare Economics and Redistribution," American Economic Journal: Microeconomics, American Economic Association, vol. 5(3), pages 180-205, August.
    2. repec:san:wpecon:1305 is not listed on IDEAS
    3. Gerasimou, Georgios, 2015. "(Hemi)continuity of additive preference preorders," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 79-81.
    4. Ranjit Vohra, 2014. "Preferences with Open Graphs: A New Result," Economics Bulletin, AccessEcon, vol. 34(4), pages 2267-2274.

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