Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty
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.
Keywordsdecision theory discrete choice monotonicity uncertainty
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- Ben-Akiva M., Lerman S.R. (1985) Discrete Choice Analysis; Theory and Application to Travel Demand. MIT Press, Cambridge, MAGoogle Scholar
- Debreu G. (1959) Theory of Value. Yale University Press, New HavenGoogle Scholar
- Karlin S., Rubin H. (1956) The theory of decision procedures for distributions with monotone likelihood ratio. Annals of Mathematical Statistics 27: 272–299Google Scholar
- Lehmann, E. (1997), Testing Statistical Hypotheses, Springer Verlag: Berlin (2nd ed.).Google Scholar
- Lindgren B. (1968) Statistical Theory. Toronto, MacmillanGoogle Scholar
- 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
- Mirrlees, J. (1987), Economic Policy and Nonrational Behaviour, WP 8728, University of California at Berkeley.Google Scholar
- 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
- 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
- Sheshinski, E. (2003), Optimal Policy to Influence Individual Choice Probabilities, Department of Economics, Hebrew University of Jerusalem.Google Scholar
- Simon C.P., Blume L. (1994) Mathematics for Economists. Norton: New YorkGoogle Scholar