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

  • Jörgen 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. Copyright Springer Science+Business Media, LLC 2007

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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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  1. James A. Mirrlees., 1987. "Economic Policy and Nonrational Behaviour," Economics Working Papers 8728, University of California at Berkeley.
  2. 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.
  3. Eytan Sheshinski, 2003. "Bounded Rationality and Socially Optimal Limits on Choice in a Self-Selection Model," CESifo Working Paper Series 868, CESifo Group Munich.
  4. 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.
  5. 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.
  6. Sheshinski, Eytan, 2000. "Optimal Policy to Influence Individual Choice Probabilities," MPRA Paper 55490, University Library of Munich, Germany, revised Dec 2002.
  7. 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.
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