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On continuity of incomplete preferences

Listed author(s):
  • Georgios Gerasimou

    ()

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

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File URL: http://hdl.handle.net/10.1007/s00355-012-0673-3
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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 41 (2013)
Issue (Month): 1 (June)
Pages: 157-167

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Handle: RePEc:spr:sochwe:v:41:y:2013:i:1:p:157-167
DOI: 10.1007/s00355-012-0673-3
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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. 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.
  3. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
  4. 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.
  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. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
  7. 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.
  8. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
  9. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
  10. 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.
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