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Almost-objective uncertainty

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  • Mark Machina

Abstract

Every subjective state space with Euclidean structure contains almost-objective events which arbitrarily closely approximate the properties of objectively uncertain events for all individuals with event-smooth betting preferences - whether or not they are expected utility, state-independent, or probabilistically sophisticated. These properties include unanimously agreed-upon revealed likelihoods, statistical independence from other subjective events, probabilistic sophistication over almost-objective bets, and linearity of state-independent and state-dependent expected utility in almost-objective likelihoods and mixtures. Most physical randomization devices are based on events of this form. Even in the presence of state-dependence, ambiguity, and ambiguity aversion, an individual’s betting preferences over almost-objective events are based solely on their attitudes toward objective risk, and can fully predict (or be predicted from) their behavior in an idealized casino. Copyright Springer-Verlag Berlin/Heidelberg 2004

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  • Mark Machina, 2004. "Almost-objective uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 1-54, July.
    • Handle: RePEc:spr:joecth:v:24:y:2004:i:1:p:1-54
    DOI: 10.1007/s00199-003-0449-1
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    1. Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2006. "Undescribable Events," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 849-868.
    2. Attanasi, Giuseppe Marco & Montesano, Aldo, 2010. "The Price for Information about Probabilities and its Relation with Capacities," TSE Working Papers 10-193, Toulouse School of Economics (TSE).
    3. 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.
    4. Fujii, Tomoki, 2017. "Dynamic Poverty Decomposition Analysis: An Application to the Philippines," World Development, Elsevier, vol. 100(C), pages 69-84.
    5. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    6. Grant, Simon & Polak, Ben, 2006. "Bayesian beliefs with stochastic monotonicity: An extension of Machina and Schmeidler," Journal of Economic Theory, Elsevier, vol. 130(1), pages 264-282, September.
    7. Noemi Pace & Giuseppe Attanasi & Christian Gollier & Aldo Montesano, 2012. "Eliciting ambiguity aversion in unknown and in compound lotteries: A KMM experimental approach," Working Papers 2012_23, Department of Economics, University of Venice "Ca' Foscari".
    8. Soo Hong Chew & Junjian Yi & Junsen Zhang & Songfa Zhong, 2016. "Education and anomalies in decision making: Experimental evidence from Chinese adult twins," Journal of Risk and Uncertainty, Springer, vol. 53(2), pages 163-200, December.
    9. John Dickhaut & Radhika Lunawat & Kira Pronin & Jack Stecher, 2011. "Decision making and trade without probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 275-288, October.
    10. Roxane Bricet, 2018. "The price for instrumentally valuable information," THEMA Working Papers 2018-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    11. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    12. Milos Borozan & Loreta Cannito & Barbara Luppi, 2022. "A tale of two ambiguities: A conceptual overview of findings from economics and psychology," Journal of Behavioral Economics for Policy, Society for the Advancement of Behavioral Economics (SABE), vol. 6(S1), pages 11-21, July.
    13. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    14. Giuseppe Attanasi & Christian Gollier & Aldo Montesano & Noemi Pace, 2014. "Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study," Theory and Decision, Springer, vol. 77(4), pages 485-530, December.
    15. ALLARD, Marie & BRONSARD, Camille & GOURIÉROUX Christian, 2003. "Aversion Analysis," Cahiers de recherche 2003-06, Universite de Montreal, Departement de sciences economiques.
      • ALLARD, Marie & BRONSARD, Camille & GOURIÉROUX, Christian, 2003. "Aversion Analysis," Cahiers de recherche 04-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    16. Giuseppe Attanasi & Aldo Montesano, 2012. "The price for information about probabilities and its relation with risk and ambiguity," Theory and Decision, Springer, vol. 73(1), pages 125-160, July.
    17. Robert Nau, 2011. "Risk, ambiguity, and state-preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 437-467, October.
    18. Soo Chew & Richard Ebstein & Songfa Zhong, 2012. "Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies," Journal of Risk and Uncertainty, Springer, vol. 44(1), pages 1-18, February.
    19. Steffen Andersen & John Fountain & Glenn Harrison & Arne Hole & E. Rutström, 2012. "Inferring beliefs as subjectively imprecise probabilities," Theory and Decision, Springer, vol. 73(1), pages 161-184, July.
    20. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    21. Nabil Al-Najjar & Luca Anderlini & Leonardo Felli, 2003. "Undescribable Contingencies," Discussion Papers 1370, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    22. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    23. Border, Kim C. & Ghirardato, Paolo & Segal, Uzi, 2005. "Objective subjective probabilities," Working Papers 1228, California Institute of Technology, Division of the Humanities and Social Sciences.

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