Weighted Sets of Probabilities and Minimax Weighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions
Year: 2012
Type: preprint
Abstract: We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure 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.
Authors: Halpern, Joseph Y., Leung, Samantha
Institution: Cornell University
Language: English
Subfield: General Decision Sciences
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: Taking Awareness, Language, and Novelty into Account in Decision-Making and Game Theory, G1523888516, RI-Small: Robust Game Theory and Decision Theory with Resource-Bounded Agents, G2633521735, G3860174062, G4099610584, G4699669188, G5001498423, G5175293516, G6495241621, G6741735475, G6782756159, G7292136116, G7452299184, G765784647, III: Large: Causal Databases, G8295926295, G8641563504, G8651238734, G8690027106, G8781524757
OpenAlex ID: W2949632474