A Theory of Case-Based Decisions [Paperback]

Itzhak Gilboa (Author), David Schmeidler (Author)

Book Description

Publication Date: September 17, 2001

Gilboa and Schmeidler provide a new paradigm for modeling decision making under uncertainty. 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. 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 to expected utility theory as well as to rule-based systems.

Editorial Reviews

Review

"This text is an excellent introduction to optimization theory." Richard A. Chechile, Journal of Mathematical Psychology

Book Description

Gilboa and Schmeidler provide a new paradigm for modeling decision making under uncertainty. 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. 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 to expected utility theory as well as to rule-based systems.

See all Editorial Reviews

Product Details

• Paperback: 210 pages
• Publisher: Cambridge University Press (September 17, 2001)
• Language: English
• ISBN-10: 0521003113
• ISBN-13: 978-0521003117
• Product Dimensions: 8.4 x 5.5 x 0.8 inches
• Shipping Weight: 10.6 ounces (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,108,074 in Books (See Top 100 in Books)

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4 of 4 people found the following review helpful:

4.0 out of 5 stars Nice theme with interesting variations---a real contribution, August 27, 2009

By 

Herbert Gintis (Northampton, MA USA) - See all my reviews

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This review is from: A Theory of Case-Based Decisions (Paperback)

Itzhak Gilboa and David Schmeidler, Theory of Case-Based Decisions (Cambridge University Press, 2001)
In his path-breaking and definitive axiomatization of Bayesian decision theory, Leonard Savage (The Foundations of Statistics, 1954) was careful to limit the proposed validity of his axioms to a "small world" context where the decision-maker is confident of the stochastic and welfare-enhancing properties of the various alternatives open to him. Gilboa and Schmeidler have no problem with this theory, but offer an alternative that is useful when dealing with decision problems that lie outside Savage's "small world." Their examples range from the mundane (buying a new car and trading in an old one, where the relevant probability distributions are unknown) to the momentous (military intervention into a civil war situation).

Gilboa and Schmeidler's alternative, given a decision problem p, is to assume the decision-maker has a repertoire M of "cases" [q,a,r], where q is another decision problem, a is the action taken in that case, and r is the result of the action. The decision-maker then forms a subjective "similarity" s[p,q], a positive number, of the current problem p with the problem q, and set the value U[a] = sum s[p,q]u[r], where u[r] is the utility of the result, and where the sum is taken over all cases [q,a,r] in the repertoire M. Finally, the decision-maker chooses the action a that maximizes U[a].

Gilboa and Schmeidler's alternative, for which they supply a plausible axiomatization, is especially useful because it dispenses with the complete knowledge assumption of the Bayesian theory in favor of the more realistic knowledge embedded in the repertoire M, which could be very small or very large, but is expressly limited by what the decision-maker actually knows.

I especially like their alternative because it is easily extended to a "social repertoire" M, in which cases include not only those experienced by the decision-mater, but also those experienced by others with whom the decision-maker is acquainted. This possibility repairs a central weakness in the Bayesian decision model, that of its failure to use the choice experience of others in updating one's own knowledge base. While Gilboa and Schmeidler do not explicitly address this possibility, their examples do. Indeed, in their example of buying a new car, they assert that Mary's expectation of getting $4000 for her old car came from (a) the "similarity" of her old car to John's old car, and (b) the fact that John got $4000 as a trade-in on his old car. Similarly, Mary expect to get her new car for $9000 because that's how much her friend Jim paid for his "similar" new car. She also believes she can borrow the $5000 difference from a bank, because her friend Sarah, who is in "similar" financial circumstances, did just that the previous week.
The only additional point missing from Gilboa and Schmeidler's account of Mary's car buying is that she must also assess the utility of the new car, and she will do that not only by reaching back into her own past experience, but also by assessing how much others "like her" in some important way have liked this car or "similar" cars. In general, the social dimension in Bayesian decision-making should extend to the assessment of utilities as well as probabilities. This is easily incorporated into Gilboa and Schmeidler's case-based decision theory.

Gilboa and Schmeidler stress that theirs is not contradictory to Bayesian theory. Indeed, if we interpret "similarity" as the "probability" that the act a will lead to the result r, then case-based leads to Bayesian decision theory, where the choice set is limited to what the decision-maker actually knows.

One of the most intriguing possibilities is that the repeated application of case-based decision-making, under appropriate conditions, might lead to standard Bayesian choices in the long run. This is especially important because, although humans are excellent Bayesian decision-makers on the level of language acquisition, word recognition, and the like, they are notoriously poor formal decision-makers, as has been repeatedly shown by Daniel Kahneman, Amos Tversky, and their colleagues. Because in real-life, most decisions depend on assessing how others have fared making "similar" decisions rather than on a purely subjective expected utility maximization, case-based reasoning may lead to quasi-Bayesian outcomes in the long run.

2 of 9 people found the following review helpful:

3.0 out of 5 stars No improvement over Keynes's analogical decision making, October 16, 2005

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Michael Emmett Brady "mandmbrady" (Bellflower, California ,United States) - See all my reviews
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This review is from: A Theory of Case-Based Decisions (Hardcover)

Gilboa and Schmeidler(GS)put forth what they claim is a new approach to decision making under uncertainty(Keynesian Uncertainty and/or Ellsbergian Ambiguity).The Case-Based Decision(CBD) approach is based on the use of analogy,similarity and induction.Decision maker's choices are based on the degree of analogy(positive and negative) with past cases stored in their memory.Actions are implemented that worked well in the past.Actions that were judged not to have been successful in the past are avoided.CBD is thus self correcting over time since decision makers can learn from experience based on the recollection of past events stored in their memories.GS's basic model is composed of two parts-memory and similarity.These two parts could be described as the basis of all analogical reasoning,which is pattern recognition.The decision maker has stored in his memory a set of what GS call triplets.Each triplet is composed of a decision problem,an action,and an outcome.Each new problem the decision maker faces is dealt with by the use of an index ranking each feasible action from low to high.The index is a weighted sum of the outcomes that have occurred in the past whenever a particular action was chosen.The weight is determined by a similarity function that measures the similarity between the new problem(case) and all the other relevant past problems(cases).A number of different possible similarity functions are put forth.Every one of these functions is additive with respect to the content of the decision makers memory of all past cases.An entire chapter is devoted to presenting an axiomatic foundation for similarity functions. The major criticism of this book is their omission of the work done in this area by John Maynard Keynes in 1921 in chapter III and Part III of the A Treatise on Probability(1921;TP).GS confine their consideration of Keynes's earlier work in this area to the following one liner."It should be mentioned that similar ideas were also expressed in the economic literature by Keynes(1921),Selten( 1978),and Cross(1983)."(2001,p.33). Keynes didn't just express"similar ideas"in the TP,which is not part of the economic literature,although much of Keynes's analysis and modeling in the TP can be applied in economics.Starting in chapter XIX of the TP,Keynes constructs a formal technical analysis of analogy in terms of propositional functions .There are two basic parts to this analysis,past experience(GS's memory)and degree of resemblance(GS's similarity).Based on an analysis using his concept of 'generalization',Keynes arrives at conclusions and results that parallel most of the conclusions arrived at by GS.One severe point of disagreement that Keynes would express would be the GS concern that the similarity functions must be additive .Additivity for Keynes would be a special case that could be attained only in the limit.In general,similarity functions will be sub additive and/or qualitative. My recommendation is that this is an excellent book for those readers who have never read the TP.However,those readers who have already digested chapters III,XVIII-XXIII of the TP will gain little additional understanding of inductive reasoning using analogy, construed as pattern recognition based on degrees of similarity,from reading GS.