By Itzhak Gilboa, David Schmeidler
Gilboa and Schmeidler supply a brand new paradigm for modeling selection making below uncertainty. Case-based determination conception means that humans make judgements via analogies to prior instances: they have a tendency to settle on acts that played good long ago in comparable events, and to prevent acts that played poorly. The authors describe the overall idea and its dating to making plans, repeated selection difficulties, inductive inference, and studying. They spotlight its mathematical and philosophical foundations and evaluate it to anticipated application conception in addition to to rule-based systems.
"This textual content is a wonderful advent to optimization theory." Richard A. Chechile, magazine of Mathematical Psychology
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Extra info for A Theory of Case-Based Decisions
46 Decision rules corresponding to negative u values, she will like an option less, the more she used it in the past, and will exhibit change seeking behavior. On the other hand, a low aspiration level, corresponding to positive u values, would make her evaluate an option more highly, the more she is familiar with it, and would result in habit formation. Chapter 6 is devoted to this interpretation. Hypothetical cases Consider the following example. Jane has to drive to the airport and she can choose between road A and road B.
More importantly, while in EUT every act is evaluated at every state, in U-maximization each act is evaluated over a different set of cases. To be precise, if a = b, the set of elements of M summed over in U(a) is disjoint from that corresponding to U(b). In particular, this set may well be empty for some a’s. On a more conceptual level, in expected utility theory the set of states is assumed to be an exhaustive list of all possible scenarios. Each state “resolves all uncertainty”, and, in particular, attaches a result to each available act.
Formally, a decision maker with memory M, similarity function s, and utility function u, who now faces a new decision problem p, will rank each act a ∈ A according to U(a) = Up,M (a) = s(p, q)u(r), (∗) (q,a,r)∈M (where the summation over the empty set is taken to yield zero), and will choose an act that maximizes this sum. Observe that, given memory M, the function U only uses the u-values of outcomes r that have appeared in M. For each act a ∈ A and each case c = (q, a, r) ∈ M in which act a was indeed chosen, one may view the product s(p, q)u(r) as the effect that case c has on the evaluation of act a in the present problem p.
A Theory of Case-Based Decisions by Itzhak Gilboa, David Schmeidler