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Multiutility representations for incomplete difference preorders

  • Pivato, Marcus

A ``difference preorder'' is a (possibly incomplete) preorder on a space of state changes (rather than the states themselves); it encodes information about preference intensity, in addition to ordinal preferences. We find necessary and sufficient conditions for a difference preorder to be representable by a family of cardinal utility functions which take values in linearly ordered abelian groups. This has applications to interpersonal comparisons, social welfare, and decisions under uncertainty.

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File URL: https://mpra.ub.uni-muenchen.de/41182/1/MPRA_paper_41182.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41182.

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Date of creation: 09 Sep 2012
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Handle: RePEc:pra:mprapa:41182
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  1. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
  2. 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.
  3. Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research.
  4. Pivato, Marcus, 2011. "Additive representation of separable preferences over infinite products," MPRA Paper 28262, University Library of Munich, Germany.
  5. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
  6. Rabin, Matthew, 1997. "Psychology and Economics," Department of Economics, Working Paper Series qt8jd5z5j2, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  7. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
  8. Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
  9. Manel Baucells & Lloyd S. Shapley, 2000. "Multiperson Utility," Econometric Society World Congress 2000 Contributed Papers 0078, Econometric Society.
  10. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
  11. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, 01.
  12. Kaushik Basu, 1982. "Determinateness of the Utility Function: Revisiting a Controversy of the Thirties," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 307-311.
  13. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 575-592, June.
  14. Christopher J. Tyson, 2007. "Cognitive Constraints, Contraction Consistency, and the Satisficing Criterion," Working Papers 614, Queen Mary University of London, School of Economics and Finance.
  15. Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information 0201001, EconWPA.
  16. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
  17. Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
  18. Patrick Suppes & Muriel Winet, 1955. "An Axiomatization of Utility Based on the Notion of Utility Differences," Management Science, INFORMS, vol. 1(3-4), pages 259-270, 04-07.
  19. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, 07.
  20. Veronika Köbberling, 2006. "Strength of preference and cardinal utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 375-391, January.
  21. Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1591-1598, March.
  22. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
  23. Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, 02.
  24. YIlmaz, Özgür, 2008. "Utility representation of lower separable preferences," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 389-394, November.
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