Cases and Scenarios in Decisions Under Uncertainty
49 Pages Posted: 7 Apr 2017
Date Written: March 17, 2017
We offer a model that combines and generalizes case-based decision theory and expected utility maximization. It is based on the premise that an agent looks ahead and assesses possible future scenarios, but may not know how to evaluate their likelihood and may not be sure that the set of scenarios is exhaustive. Consequently, she also looks back at her memory for past cases, and makes decisions so as to maximize a combined function, taking into account both scenarios and cases. We allow for non-additive set functions, both over future scenarios and over past cases, to capture (i) incompletely specified or unforeseen scenarios, (ii) ambiguity, (iii) the absence of information about counterfactuals, and (iv) some forms of case-to-rule induction ("abduction") and statistical inference. We axiomatize this model. Learning in this model takes several forms, and, in particular, changes the relative weights of the two forms of reasoning.
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