Theory and Decision

, Volume 63, Issue 2, pp 121–151 | Cite as

Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty

  • Jörgen W. Weibull
  • Lars-Göran Mattsson
  • Mark Voorneveld


It is not unusual in real-life that one has to choose among finitely many alternatives when the merit of each alternative is not perfectly known. Instead of observing the actual utilities of the alternatives at hand, one typically observes more or less precise signals that are positively correlated with these utilities. In addition, the decision-maker may, at some cost or disutility of effort, choose to increase the precision of these signals, for example by way of a careful study or the hiring of expertise. We here develop a model of such decision problems. We begin by showing that a version of the monotone likelihood-ratio property is sufficient, and also essentially necessary, for the optimality of the heuristic decision rule to always choose the alternative with the highest signal. Second, we show that it is not always advantageous to face alternatives with higher utilities, a non-monotonicity result that holds even if the decision-maker optimally chooses the signal precision. We finally establish an operational first-order condition for the optimal precision level in a canonical class of decision-problems, and we show that the optimal precision level may be discontinuous in the precision cost.


decision theory discrete choice monotonicity uncertainty 


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  1. Ben-Akiva M., Lerman S.R. (1985) Discrete Choice Analysis; Theory and Application to Travel Demand. MIT Press, Cambridge, MAGoogle Scholar
  2. Chade H., Schlee E. (2002) Another look at the Radner-Stiglitz nonconcavity in the value of information. Journal of Economic Theory 107: 421–452CrossRefGoogle Scholar
  3. Debreu G. (1959) Theory of Value. Yale University Press, New HavenGoogle Scholar
  4. Karlin S., Rubin H. (1956) The theory of decision procedures for distributions with monotone likelihood ratio. Annals of Mathematical Statistics 27: 272–299Google Scholar
  5. Kihlstrom R. (1974a) A Bayesian model of demand for information about product quality. International Economic Review 15: 99–118CrossRefGoogle Scholar
  6. Kihlstrom R. (1974b) A general theory of demand for information about product quality. Journal of Economic Theory 8: 413–439CrossRefGoogle Scholar
  7. Lehmann, E. (1997), Testing Statistical Hypotheses, Springer Verlag: Berlin (2nd ed.).Google Scholar
  8. Lindgren B. (1968) Statistical Theory. Toronto, MacmillanGoogle Scholar
  9. McFadden D. (1973) Conditional logit analysis of qualitative choice behavior. In: Zaremka P. (eds). Frontiers in Econometrics. Academic Press, New York, pp. 105–142Google Scholar
  10. Milgrom P. (1981) Good news and bad news: Representation theorems and applications. Bell Journal of Economics 12: 380–391CrossRefGoogle Scholar
  11. Mirrlees, J. (1987), Economic Policy and Nonrational Behaviour, WP 8728, University of California at Berkeley.Google Scholar
  12. Radner, R. and Stiglitz, J. (1984), A nonconcavity in the value of information, in Boyer, M. and Kihlstrom, R.E. (eds.), Bayesian Models in Economic Theory. North-Holland: Amsterdam, pp. 33–52.Google Scholar
  13. Sheshinski, E. (2002), Bounded Rationality and Socially Optimal Limits on Choice in a Self-Selection Model, Department of Economics, Hebrew University of Jerusalem.Google Scholar
  14. Sheshinski, E. (2003), Optimal Policy to Influence Individual Choice Probabilities, Department of Economics, Hebrew University of Jerusalem.Google Scholar
  15. Simon C.P., Blume L. (1994) Mathematics for Economists. Norton: New YorkGoogle Scholar
  16. Vega-Redondo F. (1993) Simple and inertial behavior: an optimizing decision model with imprecise perceptions. Economic Theory 3: 87–98CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jörgen W. Weibull
    • 1
  • Lars-Göran Mattsson
    • 2
  • Mark Voorneveld
    • 3
    • 4
  1. 1.Department of EconomicsStockholm School of EconomicsStockholmSweden
  2. 2.Department of Transport and EconomicsRoyal Institute of TechnologyStockholmSweden
  3. 3.Department of EconomicsStockholm School of EconomicsStockholmSweden
  4. 4.Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands

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