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Multiple solutions under quasi-exponential discounting

Author

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  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Jörgen Weibull

    (Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, SSE - Department of Economics - Stockholm School of Economics)

Abstract

We consider a group or committee that faces a binary decision under uncertainty. Each member holds some private information. Members agree which decision should be taken in each state of nature, had this been known, but they may attach different values to the two types of mistake that may occur. Most voting rules have a plethora of uninformative equilibria, and informative voting may be incompatible with equilibrium. We analyze an anonymous randomized majority rule that has a unique equilibrium. This equilibrium is strict, votes are informative, and the equilibrium implements the optimal decision with probability one in the limit as the committee size goes to infinity. We show that this also holds for the usual majority rule under certain perturbations of the behavioral assumptions: (i) a slight preference for voting according to one's conviction, and (ii) transparency and a slight preference for esteem. We also show that a slight probability for voting mistakes strengthens the incentive for informative voting.

Suggested Citation

  • Nicolas Vieille & Jörgen Weibull, 2008. "Multiple solutions under quasi-exponential discounting," Working Papers hal-00354231, HAL.
  • Handle: RePEc:hal:wpaper:hal-00354231
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00354231
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    2. Guo, Nick L. & Caliendo, Frank N., 2014. "Time-inconsistent preferences and time-inconsistent policies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 102-108.
    3. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    4. Jamison, Julian & Wegener, Jon, 2010. "Multiple selves in intertemporal choice," Journal of Economic Psychology, Elsevier, vol. 31(5), pages 832-839, October.
    5. repec:eee:matsoc:v:87:y:2017:i:c:p:40-54 is not listed on IDEAS
    6. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    7. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2015. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Papers 1504.01152, arXiv.org, revised May 2015.
    8. Peeters R.J.A.P. & Méder Z.Z. & Flesch J., 2014. "Naiveté and sophistication in dynamic inconsistency," Research Memorandum 005, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    uniqueness; : time-consistency; hyperbolic discounting; stochastic dynamic programming; multiplicity; uniqueness.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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