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

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Author Info
Jörgen Weibull ()
Lars-Göran Mattsson
Mark Voorneveld

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Abstract

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. Copyright Springer Science+Business Media, LLC 2007

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File URL: http://hdl.handle.net/10.1007/s11238-007-9041-7
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Publisher Info
Article provided by Springer in its journal Theory and Decision.

Volume (Year): 63 (2007)
Issue (Month): 2 (September)
Pages: 121-151
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Handle: RePEc:kap:theord:v:63:y:2007:i:2:p:121-151

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Web page: http://www.springerlink.com/link.asp?id=100341

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Related research
Keywords: decision theory; discrete choice; monotonicity; uncertainty;

References listed on IDEAS
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  1. Vega-Redondo, Fernando, 1993. "Simple and Inertial Behavior: An Optimizing Decision Model with Imprecise Perceptions," Economic Theory, Springer, vol. 3(1), pages 87-98, January.
  2. Kihlstrom, Richard, 1974. "A general theory of demand for information about product quality," Journal of Economic Theory, Elsevier, vol. 8(4), pages 413-439, August. [Downloadable!] (restricted)
  3. Kihlstrom, Richard E, 1974. "A Bayesian Model of Demand for Information About Product Quality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 99-118, February. [Downloadable!] (restricted)
  4. James A. Mirrlees., 1987. "Economic Policy and Nonrational Behaviour," Economics Working Papers 8728, University of California at Berkeley.
  5. Eytan Sheshinski, 2000. "Bounded Rationality and Socially Optimal Limits on Choice in a Self-Selection Model," Discussion Paper Series dp330, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem, revised Nov 2002. [Downloadable!]
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  6. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn. [Downloadable!] (restricted)
    Other versions:
  7. Chade, Hector & Schlee, Edward, 2002. "Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 421-452, December. [Downloadable!] (restricted)
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