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On attitude polarization under Bayesian learning with non-additive beliefs

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  • Alexander Zimper

    ()

  • Alexander Ludwig

    ()

Abstract

Ample psychological evidence suggests that people’s learning behavior is often prone to a "myside bias" or "irrational belief persistence" in contrast to learning behavior exclusively based on objective data. In the context of Bayesian learning such a bias may result in diverging posterior beliefs and attitude polarization even if agents receive identical information. Such patterns cannot be explained by the standard model of rational Bayesian learning that implies convergent beliefs. As our key contribution, we therefore develop formal models of Bayesian learning with psychological bias as alternatives to rational Bayesian learning. We derive conditions under which beliefs may diverge in the learning process despite the fact that all agents observe the same - arbitrarily large - sample, which is drawn from an "objective" i.i.d. process. Furthermore, one of our learning scenarios results in attitude polarization even in the case of common priors. Key to our approach is the assumption of ambiguous beliefs that are formalized as non-additive probability measures arising in Choquet expected utility theory. As a specific feature of our approach, our models of Bayesian learning with psychological bias reduce to rational Bayesian learning in the absence of ambiguity.
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Suggested Citation

  • Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
  • Handle: RePEc:kap:jrisku:v:39:y:2009:i:2:p:181-212
    DOI: 10.1007/s11166-009-9074-0
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    as
    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    3. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    4. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
    5. Abel, Andrew B., 2002. "An exploration of the effects of pessimism and doubt on asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1075-1092, July.
    6. Fernández, Raquel & Levy, Gilat, 2008. "Diversity and redistribution," Journal of Public Economics, Elsevier, vol. 92(5-6), pages 925-943, June.
    7. Lindqvist, Erik & Östling, Robert, 2010. "Political Polarization and the Size of Government," American Political Science Review, Cambridge University Press, vol. 104(03), pages 543-565, August.
    8. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    9. Alexander Ludwig & Alexander Zimper, 2008. "A Parsimonious Choquet Model of Subjective Life Expectancy," Working Papers, Center for Retirement Research at Boston College wp2008-20, Center for Retirement Research, revised Dec 2008.
    10. Tonks, Ian, 1983. "Bayesian Learning and the Optimal Investment Decision of the Firm," Economic Journal, Royal Economic Society, vol. 93(369a), pages 87-98, Supplemen.
    11. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    12. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    13. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    14. Kandel, Eugene & Pearson, Neil D, 1995. "Differential Interpretation of Public Signals and Trade in Speculative Markets," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 831-872, August.
    15. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    16. Viscusi, W. Kip, 1985. "A Bayesian perspective on biases in risk perception," Economics Letters, Elsevier, vol. 17(1-2), pages 59-62.
    17. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1275-1303.
    18. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    19. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    20. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-250, July-Aug..
    21. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    22. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    23. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    24. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    25. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    26. Pok-sang Lam & Stephen G. Cecchetti & Nelson C. Mark, 2000. "Asset Pricing with Distorted Beliefs: Are Equity Returns Too Good to Be True?," American Economic Review, American Economic Association, vol. 90(4), pages 787-805, September.
    27. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    28. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    29. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
    30. Viscusi, W Kip & O'Connor, Charles J, 1984. "Adaptive Responses to Chemical Labeling: Are Workers Bayesian Decision Makers?," American Economic Review, American Economic Association, vol. 74(5), pages 942-956, December.
    31. Kurz, Mordecai, 1996. "Rational Beliefs and Endogenous Uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 383-397, October.
    32. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    33. Alberto Alesina & Reza Baqir & William Easterly, 1999. "Public Goods and Ethnic Divisions," The Quarterly Journal of Economics, Oxford University Press, vol. 114(4), pages 1243-1284.
    34. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    35. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    36. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    37. Matthew Rabin & Joel L. Schrag, 1999. "First Impressions Matter: A Model of Confirmatory Bias," The Quarterly Journal of Economics, Oxford University Press, vol. 114(1), pages 37-82.
    38. Neeman, Zvika, 1996. "Approximating Agreeing to Disagree Results with Commonp-Beliefs," Games and Economic Behavior, Elsevier, vol. 12(1), pages 162-164, January.
    39. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    40. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    41. Alon Brav & J.B. Heaton, 2002. "Competing Theories of Financial Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 575-606, March.
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    Citations

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    Cited by:

    1. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    2. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    3. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-1007-y is not listed on IDEAS
    4. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 97-115, April.
    5. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    6. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    7. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    8. Sandeep Baliga & Eran Hanany & Peter Klibanoff, 2013. "Polarization and Ambiguity," Discussion Papers 1558, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Alexander Zimper & Wei Ma, 2017. "Bayesian learning with multiple priors and nonvanishing ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 409-447, October.
    10. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    11. Aylit Tina Romm, 2014. "An interpretation of focal point responses as non-additive beliefs," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(5), pages 387-402, September.
    12. Enrica Carbone & Konstantinos Georgalos & Gerardo Infante, 2016. "Individual vs. Group Decision Making: an Experiment on Dynamic Choice under Risk and Ambiguity," Working Papers 138739716, Lancaster University Management School, Economics Department.
    13. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.

    More about this item

    Keywords

    Non-additive probability measures; Choquet expected utility theory; Bayesian learning; Bounded rationality; C79; D83;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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