The value of useless information

Alaoui, Larbi (2008): The value of useless information.

Abstract

There are a number of cases in which individuals do not expect to find out which outcome occurs. The standard von Neumann-Morgenstern Expected Utility model cannot be used in these cases, since it does not distinguish between lotteries for which the outcomes are observed by the agent and lotteries for which they are not. This paper provides an axiomatic model that makes this distinction. A representation theorem is then obtained. This framework admits preferences for observing the outcome, and preferences for remaining in doubt. Doubt-proneness and doubt-aversion are defined, and the relation between risk-aversion, caution and doubt-attitude is explored. The model builds on the standard vNM framework, but other frameworks can also be extended to allow for preferences for observing the outcomes and preferences for remaining in doubt. A methodology for this extension is also provided. This framework can accommodate behavioral patterns that are inconsistent with the vNM model, and which have let to significantly different models. In particular, this framework accommodates self-handicapping, in which an agent chooses to impair his own performance. It also admits a status-quo bias, even though it does not allow for framing effects. In a political economy setting, voters have incentive to remain ignorant even if information is costless.

• Item Type: MPRA Paper
• Language: English
• Keywords: Decision theory; Value of information; Doubt; Unobserved outcomes; Unresolved lotteries
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General

References

[1] M. Abdellaoui. A genuine rank-dependent generalization of the von Neumann- Morgenstern expected utility theorem. Econometrica, 70(2):717–736, 2002.

[2] S. Adam, S. Wiggins, P Whyte, M. Bloch, M. Shokeir, H. Soltan, W. Meschino, A. Summers, O. Suchowersky, J. Welch, M. Huggins, J. Theilmann, and M. Hayden. Five year study of prenatal testing for huntington’s disease: demand, attitudes, and psychological assessment. Journal of Medical Genetics, 30:549–556, 1993.

[3] G. Akerlof and W. Dickens. The economic consequences of cognitive dissonance. American Economic Review, 72(3):307–319, 1982.

[4] M. Allais. Le comportement de l’homme rationnel devant le risque: Critique des postulats de l’ecole americaine. Econometrica, 21(4):503–546, 1953.

[5] L. Bartels. Uninformed votes: Informational effects in presidential elections. American Journal of Political Science, 40(1):194–230, 1996.

[6] D. Bell. Regret in decision making under uncertainty. Operations Research, 30:961– 981, 1982.

[7] D. Bell and P. Fishburn. Probability weights in rank-dependent utility with binary even-chance independence. Journal of Mathematical Psychology, 47:244–258, 2003.

[8] R. Benabou. Ideology. Journal of the European Economic Association (Forthcoming), 2008.

[9] R. Benabou and J. Tirole. Self-confidence and personal motivation. Quartely Journal of Economics, 117(3):871–915, 2002.

[10] R. Benabou and J. Tirole. Belief in a just world and redistributive politics. Quartely Journal of Economics, 121(2):699–746, 2006.

[11] R. Benabou and J. Tirole. Identity, dignity and taboos: Beliefs as assets. 2006.

[12] S. Berglas and E. Jones. Drug choice as a self-handicapping strategy in response to noncontingent success. Journal of Personality and Social Psychology, 36(4):405–417, 1978.

[13] M. Brunnermeier and J. Parker. Optimal expectations. American Economic Review, 95(4):1092–1118, 2005.

[14] A. Caplin and J. Leahy. Psychological expected utility theory and anticipatory feelings. Quartely Journal of Economics, 116(1):55–79, 2001.

[15] J. Carrillo and T. Mariotti. Strategic ignorance as a self-disciplining device. Review of Economic Studies, 67:529–544, 2000.

[16] S. H. Chew, E. Karni, and Z. Safra. Risk aversion in the theory of expected utility with rank dependent probabilities. Journal of Economic Theory, 42:370–381, 1986.

[17] O. Compte and A. Postlewaite. Confidence-enhanced performance. American Economic Review, 94(5):1536–1557, 2004.

[18] E. Dekel. An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. Journal of Economic Theory, 40:304–318, 1986.

[19] E. Diecidue and P. Wakker. On the intuition of rank-dependent utility. Journal of Risk and Uncertainty, 23(3):281–298, 2001.

[20] D. Dillenberger. Preferences for one-shot resolution of uncertainty and allais-type behavior. Working paper, 2008.

[21] R. Dudley. Real Analysis and Probability. Cambridge University Press, New York NY, 2002.

[22] D. Ellsberg. Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75(4):643–669, 1961.

[23] D. Ellsberg. Risk, Ambiguity and Decision. Garland Publishing, New York NY, 2001.

[24] I. Good. Good Thinking: The Foundations of Probability and Its Applications. University of Minnesota Press, 1983.

[25] S. Grant, A. Kajii, and B. Polak. Intrinsic preference for information. Journal of Economic Theory, 83:233–259, 1998.

[26] S. Grant, A. Kajii, and B. Polak. Temporal resolution of uncertainty and recursive non-expected utility models. Econometrica, 68(2):425–434, 2000.

[27] F. Gul. A theory of disappointment aversion. Econometrica, 59(3):667–686, 1991.

[28] M. Hemphill. Pretesting for huntington’s disease: An overview. Hastings Center Report, 3(3):12–13, 1973.

[29] D. Kahneman, J. Knetsch, and R. Thaler. Anomalies: The endowment effect, loss aversion, and status quo bias. Journal of Economic Perspectives, 5(1):193–206, 1991.

[30] E. Karni. Decision Making Under Uncertainty. Harvard University Press, Cambridge MA, 1985.

[31] E. Karni and Z. Safra. Rank-dependent probabilities. Economic Journal, 100(401):487–495, 1990.

[32] B. Koszegi. Ego utility, overconfidence, and task choice. Journal of the European Economic Association, 4(4):673–707, 2006.

[33] D. Kreps. Notes on the Theory of Choice. Westview Press, Boulder CO, 1988.

[34] D. Kreps and E. Porteus. Temporal resolution of uncertainty and dynamic choice theory. Econometrica, 46(1):185–200, 1978.

[35] G. Loomes and Sugden R. Regret theory: An alternative theory of rational choice under uncertainty. The Economic Journal, 92(368):805–824, 1982.

[36] M. Machina. Choice under uncertainty: Problems solved and unsolved. Economic Perspectives, 1(1):121–154, 1987.

[37] M. Machina. Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature, XXVII:1622–1668, 1989.

[38] S. Pinker. The Stuff of Thought. Penguin Group, New York NY, 2007.

[39] D. Prelec. The probability weighting function. Econometrica, 66(3):497–527, 1998.

[40] J. Quiggin. A theory of anticipated utility. Journal of Economic Behavior and Organization, 3:323–343, 1982.

[41] W. Samuelson and R. Zeckhauser. Status quo bias in decision making. Journal of Risk and Uncertainty, 1:7–59, 1988.

[42] L. Savage. The Foundations of Statistics. Dover Publications, New York NY, 1972.

[43] U. Segal. Two-stage lotteries without the reduction axiom. Econometrica, 58(2):349–377, 1990.

[44] L. Selden. A new representation of preferences over ”certain x uncertain” consumption pairs: The ”ordinal certainty equivalent” hypothesis. Econometrica, 46(5):1045–1060, 1978.

[45] R. Sugden. An axiomatic foundation for regret theory. Journal of Economic Theory, 60:159–180, 1993.

[46] A Tyler, O. Quarrell, L. Lazarou, A. Meredith, and P. Harper. Exclusion testing in pregnancy for huntington’s disease. Journal of Medical Genetics, 27:488–495, 1990.

[47] P. Wakker. Separating marginal utility and probabilistic risk aversion. Theory and Decision, 36:1–44, 1994.

[48] M. Yaari. The dual theory of choice under risk. Econometrica, 55(1):95–115, 1987.

[49] M. Zeelenberg. Anticipated regret, expected feedback and behavioral decision making. Journal of Behavioral Decision Making, 12:93–106, 1999.