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Multiple solutions under quasi-exponential discounting

Author

Listed:
  • 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, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Jörgen Weibull

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris, SSE - Department of Economics - SSE - 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.science/hal-00354231
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    References listed on IDEAS

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    Cited by:

    1. Hideyuki Kamiryo, 2014. "Earth Endogenous System: To Answer the Current Unsolved Economic Problems (Second Edition)," Earth Endogenous System: To Answer the Current Unsolved Economic Problems (Second Edition), Better Advances Press, Canada, edition 2, volume 2, number 01 edited by Dr. Yisheng Huang, May.
    2. repec:bap:ees2th:01 is not listed on IDEAS
    3. Bernergård, Axel, 2019. "Self-control problems and the folk theorem," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 332-347.
    4. repec:bap:eebook:02 is not listed on IDEAS
    5. Mariana Khapko, 2023. "Asset pricing with dynamically inconsistent agents," Finance and Stochastics, Springer, vol. 27(4), pages 1017-1046, October.
    6. Jean-Pierre Drugeon & Bertrand Wigniolle, 2021. "On Markovian collective choice with heterogeneous quasi-hyperbolic discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1257-1296, November.
    7. Jamison, Julian & Wegener, Jon, 2010. "Multiple selves in intertemporal choice," Journal of Economic Psychology, Elsevier, vol. 31(5), pages 832-839, October.
    8. Camilo Hern'andez & Dylan Possamai, 2020. "Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents," Papers 2002.12572, arXiv.org, revised Jul 2021.
    9. Kyle Hyndman & Alberto Bisin, 2022. "Procrastination, self-imposed deadlines and other commitment devices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 871-897, October.
    10. Méder, Zsombor Z. & Flesch, János & Peeters, Ronald, 2017. "Naiveté and sophistication in dynamic inconsistency," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 40-54.
    11. Caliendo, Frank N. & Findley, T. Scott, 2019. "Commitment and welfare," Journal of Economic Behavior & Organization, Elsevier, vol. 159(C), pages 210-234.
    12. Kang, Minwook & Kim, Eungsik, 2023. "A government policy with time-inconsistent consumers," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 44-67.
    13. 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.
    14. Hideyuki Kamiryo, 2014. "Earth Endogenous System: To Answer the Current Unsolved Economic Problems (Second Edition)," Earth Endogenous System: To Answer the Current Unsolved Economic Problems (Second Edition), Better Advances Press, Canada, edition 2, volume 2, number 02 edited by Yisheng Huang, May.
    15. Xue Dong He & Zhaoli Jiang & Steven Kou, 2020. "Portfolio Selection under Median and Quantile Maximization," Papers 2008.10257, arXiv.org, revised Mar 2021.
    16. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Haiyang Wang & Zhen Wu, 2014. "Partially Observed Time-Inconsistency Recursive Optimization Problem and Application," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 664-687, May.
    22. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.

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    More about this item

    Keywords

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

    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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