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

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  • Jörgen Weibull
  • 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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    Cited by:

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    5. Duffy, Sean & Gussman, Steven & Smith, John, 2021. "Visual judgments of length in the economics laboratory: Are there brains in stochastic choice?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).
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    7. Jun Chen, 2021. "The Condorcet Jury Theorem with Information Acquisition," Games, MDPI, vol. 12(4), pages 1-33, October.
    8. Friedman, Evan, 2020. "Endogenous quantal response equilibrium," Games and Economic Behavior, Elsevier, vol. 124(C), pages 620-643.
    9. Lindbeck, Assar & Weibull, Jörgen, 2015. "Pay Schemes, Bargaining, and Competition for Talent," Working Paper Series 1100, Research Institute of Industrial Economics.
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    11. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.

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