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Quasiconcave preferences on the probability simplex: A nonparametric analysis

  • Heufer, Jan

A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasiconcave preferences. Necessary and sufficient conditions are presented which can easily be tested. If the answer is affirmative, the methods developed here allow us to reconstruct bounds on indifference curves. Furthermore we can construct quasiconcave utility functions in analogy to the utility function constructed in the proof of Afriat’s Theorem. The approach is of interest for ex ante fairness considerations when a dictator is asked to choose probabilities to win an indivisible prize. It is also of interest for decisions under risk and stochastic choice. It allows nonparametric interpersonal comparisons.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 65 (2013)
Issue (Month): 1 ()
Pages: 21-30

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Handle: RePEc:eee:matsoc:v:65:y:2013:i:1:p:21-30
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  1. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  2. Wulf Albers & Robin Pope & Reinhard Selten & Bodo Vogt, 2000. "Experimental Evidence for Attractions to Chance," German Economic Review, Verein für Socialpolitik, vol. 1(2), pages 113-130, 05.
  3. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
  4. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
  5. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-96, March.
  6. Raymond Fisman & Shachar Kariv & Daniel Markovits, 2007. "Individual Preferences for Giving," American Economic Review, American Economic Association, vol. 97(5), pages 1858-1876, December.
  7. Jean Fernand Nguema, 2003. "Sense of impartiality," Economics Bulletin, AccessEcon, vol. 4(31), pages 1-7.
  8. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Economics Papers from University Paris Dauphine 123456789/4099, Paris Dauphine University.
  9. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-63, January.
  10. Knoblauch, Vicki, 1992. "A Tight Upper Bound on the Money Metric Utility Function," American Economic Review, American Economic Association, vol. 82(3), pages 660-63, June.
  11. Shasikanta Nandeibam, 2009. "On probabilistic rationalizability," Social Choice and Welfare, Springer, vol. 32(3), pages 425-437, March.
  12. Jan Heufer, 2009. "Stochastic homothetically revealed preference for tight stochastic demand functions," Economics Bulletin, AccessEcon, vol. 29(3), pages 2472-2477.
  13. Sopher & Narramore, 2000. "Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study," Theory and Decision, Springer, vol. 48(4), pages 323-349, June.
  14. Edi Karni & Zvi Safra, 2002. "Individual Sense of Justice: A Utility Representation," Econometrica, Econometric Society, vol. 70(1), pages 263-284, January.
  15. Martin Sandbu, 2008. "Axiomatic foundations for fairness-motivated preferences," Social Choice and Welfare, Springer, vol. 31(4), pages 589-619, December.
  16. Alexander W. Cappelen & James Konow & Erik ?. S?rensen & Bertil Tungodden, 2013. "Just Luck: An Experimental Study of Risk-Taking and Fairness," American Economic Review, American Economic Association, vol. 103(4), pages 1398-1413, June.
  17. Edi Karni & Zvi Safra, 2008. "Moral sentiments and social choice," Social Choice and Welfare, Springer, vol. 30(3), pages 427-446, April.
  18. William Neilson, 2006. "Axiomatic reference-dependence in behavior toward others and toward risk," Economic Theory, Springer, vol. 28(3), pages 681-692, 08.
  19. Karni, Edi & Safra, Zvi, 2002. "Intensity of the Sense of Fairness: Measurement and Behavioral Characterization," Journal of Economic Theory, Elsevier, vol. 105(2), pages 318-337, August.
  20. Barry Sopher & Edi Karni & Tim Salmon, 2001. "Individual Sense of Fairness: An Experimental Study," Departmental Working Papers 200107, Rutgers University, Department of Economics.
  21. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
  22. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer, vol. 23(3), pages 589-599, March.
  23. Kalandrakis, Tasos, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
  24. Varian, Hal R, 1983. "Non-Parametric Tests of Consumer Behaviour," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 99-110, January.
  25. Jan Heufer, 2011. "Stochastic revealed preference and rationalizability," Theory and Decision, Springer, vol. 71(4), pages 575-592, October.
  26. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Levine's Bibliography 321307000000000793, UCLA Department of Economics.
  27. Rosa L. Matzkin & Marcel K. Richter, 1987. "Testing Strictly Concave Rationality," Cowles Foundation Discussion Papers 844, Cowles Foundation for Research in Economics, Yale University.
  28. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  29. repec:ebl:ecbull:v:4:y:2003:i:31:p:1-7 is not listed on IDEAS
  30. James Andreoni & John Miller, 2002. "Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism," Econometrica, Econometric Society, vol. 70(2), pages 737-753, March.
  31. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May.
  32. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  33. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
  34. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
  35. Douglas M. Gale & Shachar Kariv & Syngjoo Choi & Raymond Fisman, 2007. "Revealing Preferences Graphically: An Old Method Gets a New Tool Kit," American Economic Review, American Economic Association, vol. 97(2), pages 153-158, May.
  36. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-94, September.
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