A Theory of Case-Based Decisions

by Itzhak Gilboa , David Schmeidler

• ISBN13: 9780521003117
• ISBN10: 0521003113
• Format: Paperback
• Copyright: 2001-09-17
• Publisher: Cambridge University Press

Summary

Gilboa and Schmeidler provide a new paradigm for modelling decision making under uncertainty. Unlike the classical theory of expected utility maximization, case-based decision theory does not assume that decision makers know the possible 'states of the world' or the outcomes, let alone the decision matrix attaching outcomes to act-state pairs. Case-based decision theory suggests that people make decisions by analogies to past cases: they tend to choose acts that performed well in the past in similar situations, and to avoid acts that performed poorly. It is an alternative to expected utility theory when both states of the world and probabilities are neither given in the problem nor can be easily constructed. The authors describe the general theory and its relationship to planning, repeated choice problems, inductive inference, and learning; they highlight its mathematical and philosophical foundations and compare it with expected utility theory as well as with rule-based systems.

Table of Contents

Acknowledgments	x
1 Prologue	1	(28)
The scope of this book	1	(3)
Meta-theoretical vocabulary	4	(18)
Theories and conceptual frameworks	4	(4)
Descriptive and normative theories	8	(4)
Axiomatizations	12	(4)
Behaviorist, behavioral, and cognitive theories	16	(1)
Rationality	17	(2)
Deviations from rationality	19	(1)
Subjective and objective terms	20	(2)
Meta-theoretical prejudices	22	(7)
Preliminary remark on the philosophy of science	22	(1)
Utility and expected utility ``theories'' as conceptual frameworks and as theories	23	(2)
On the validity of purely behavioral economic theory	25	(2)
What does all this have to do with CBDT?	27	(2)
2 Decision rules	29	(33)
Elementary formula and interpretations	29	(18)
Motivating examples	29	(5)
Model	34	(5)
Aspirations and satisficing	39	(4)
Comparison with EUT	43	(3)
Comments	46	(1)
Variations and generalizations	47	(6)
Average similarity	47	(2)
Act similarity	49	(3)
Case similarity	52	(1)
CBDT as a behaviorist theory	53	(6)
W-maximization	53	(2)
Cognitive specification: EUT	55	(1)
Cognitive specification: CBDT	56	(1)
Comparing the cognitive specifications	57	(2)
Case-based prediction	59	(3)
3 Axiomatic derivation	62	(29)
Highlights	62	(2)
Model and result	64	(9)
Axioms	65	(2)
Basic result	67	(1)
Learning new cases	68	(1)
Equivalent cases	69	(2)
U-maximization	71	(2)
Discussion of the axioms	73	(4)
Proofs	77	(14)
4 Conceptual foundations	91	(18)
CBDT and expected utility theory	91	(7)
Reduction of theories	91	(2)
Hypothetical reasoning	93	(2)
Observability of data	95	(1)
The primacy of similarity	96	(1)
Bounded rationality?	97	(1)
CBDT and rule-based systems	98	(11)
What can be known?	98	(2)
Deriving case-based decision theory	100	(5)
Implicit knowledge of rules	105	(2)
Two roles of rules	107	(2)
5 Planning	109	(16)
Representation and evaluation of plans	109	(10)
Dissection, selection, and recombination	109	(3)
Representing uncertainty	112	(2)
Plan evaluation	114	(4)
Discussion	118	(1)
Axiomatic derivation	119	(6)
Set-up	119	(2)
Axioms and result	121	(2)
Proof	123	(2)
6 Repeated choice	125	(21)
Cumulative utility maximization	125	(11)
Memory-dependent preferences	125	(2)
Related literature	127	(2)
Model and results	129	(4)
Comments	133	(1)
Proofs	134	(2)
The potential	136	(10)
Definition	136	(2)
Normalized potential and neo-classical utility	138	(3)
Substitution and complementarity	141	(5)
7 Learning and induction	146	(43)
Learning to maximize expected payoff	146	(28)
Aspiration-level adjustment	146	(1)
Realism and ambitiousness	147	(3)
Highlights	150	(3)
Model	153	(3)
Results	156	(2)
Comments	158	(3)
Proofs	161	(13)
Learning the similarity function	174	(9)
Examples	174	(3)
Counter-example to U-maximization	177	(4)
Learning and expertise	181	(2)
Two views of induction: CBDT and simplicism	183	(6)
Wittgenstein and Hume	183	(1)
Examples	184	(5)
Bibliography	189	(8)
Index	197