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Extended Relative Maximum Likelihood Updating of Choquet Beliefs

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  • Xiaoyu Cheng

Abstract

Cheng(2021) proposes and characterizes Relative Maximum Likelihood (RML) updating rule when the ambiguous beliefs are represented by a set of priors. Relatedly, this note proposes and characterizes Extended RML updating rule when the ambiguous beliefs are represented by a convex capacity. Two classical updating rules for convex capacities, Dempster-Shafer (Shafer, 1976) and Fagin-Halpern rules (Fagin and Halpern, 1990) are included as special cases of Extended RML.

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  • Xiaoyu Cheng, 2021. "Extended Relative Maximum Likelihood Updating of Choquet Beliefs," Papers 2109.02597, arXiv.org.
    • Handle: RePEc:arx:papers:2109.02597
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    References listed on IDEAS

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    1. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
    2. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Xiaoyu Cheng, 2019. "Relative Maximum Likelihood Updating of Ambiguous Beliefs," Papers 1911.02678, arXiv.org, revised Oct 2021.
    5. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    Cited by:

    1. Xiaoyu Cheng, 2022. "Robust Data-Driven Decisions Under Model Uncertainty," Papers 2205.04573, arXiv.org.
    2. Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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