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

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  • Jörgen Weibull

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  • Lars-Göran Mattsson
  • Mark Voorneveld

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

Suggested Citation

  • Jörgen Weibull & Lars-Göran Mattsson & Mark Voorneveld, 2007. "Better May be Worse: Some Monotonicity Results and Paradoxes in Discrete Choice Under Uncertainty," Theory and Decision, Springer, vol. 63(2), pages 121-151, September.
  • Handle: RePEc:kap:theord:v:63:y:2007:i:2:p:121-151
    DOI: 10.1007/s11238-007-9041-7
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    References listed on IDEAS

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    1. Mirrlees, James A., 1987. "Economic Policy and Nonrational Behavior," Department of Economics, Working Paper Series qt9tw447ws, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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    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.
    4. Sheshinski, Eytan, 2000. "Bounded Rationality and Socially Optimal Limits on Choice in A Self-Selection Model," MPRA Paper 56141, University Library of Munich, Germany, revised Nov 2002.
    5. 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.
    6. Sheshinski, Eytan, 2000. "Optimal Policy to Influence Individual Choice Probabilities," MPRA Paper 55490, University Library of Munich, Germany, revised Dec 2002.
    7. Vega-Redondo, Fernando, 1993. "Simple and Inertial Behavior: An Optimizing Decision Model with Imprecise Perceptions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 87-98, January.
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    Cited by:

    1. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    2. Mark Voorneveld & Jörgen W. Weibull, 2011. "A Scent of Lemon—Seller Meets Buyer with a Noisy Quality Observation," Games, MDPI, Open Access Journal, vol. 2(1), pages 1-24, March.
    3. Lindbeck, Assar & Weibull, Jörgen, 2015. "Pay Schemes, Bargaining, and Competition for Talent," Working Paper Series 1100, Research Institute of Industrial Economics.
    4. Lindbeck, Assar & Weibull, Jörgen, 2017. "Investment, Rational Inattention, and Delegation," Working Paper Series 1171, Research Institute of Industrial Economics.

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