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Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions

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  • Joseph Y. Halpern
  • Samantha Leung

Abstract

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making-minimizing expected regret-to obtain minimax weighted expected regret (MWER).We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

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  • Joseph Y. Halpern & Samantha Leung, 2012. "Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions," Papers 1210.4853, arXiv.org.
  • Handle: RePEc:arx:papers:1210.4853
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    References listed on IDEAS

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    Cited by:

    1. Joseph Y. Halpern & Samantha Leung, 2016. "Maxmin weighted expected utility: a simpler characterization," Theory and Decision, Springer, vol. 80(4), pages 581-610, April.
    2. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    3. Kaiwen Li & Yuanming Song & Rui Wang, 2022. "Multi-Objective Optimal Sizing of HRES under Multiple Scenarios with Undetermined Probability," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    4. Karmellos, M. & Georgiou, P.N. & Mavrotas, G., 2019. "A comparison of methods for the optimal design of Distributed Energy Systems under uncertainty," Energy, Elsevier, vol. 178(C), pages 318-333.

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