Gilboa, I., Schmeidler, D.: Case-based decision theory. Quarterly Journal of Economics 110 (1995) 605--639  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the literature on on line algorithms [4] and is presented in [18] Our representation theorem is the rst to introduce a Savage style axiomatization (i.e. where utilities are ascribed to the agents) for this basic and widely used decision criterion. Recent work by Gilboa and Schmeidler [26] examines case based decision making, which should be of interest to researchers in qualitative decision theory. 22 Although researchers in arti cial intelligence (and to some extent statisticians) have examined and used various qualitative notions of knowledge, belief (e.g. 12, 29, 8] and ....

I. Gilboa and D. Schmeidler. Case-based decision theory. The Quarterly Journal of Economics, 110:605-639, 1995.

....in the literature on on line algorithms [4] and is presented in [18] Our representation theorem is the first to introduce a Savage style axiomatization (i.e. where utilities are ascribed to the agents) for this basic and widely used decision criterion. Recent work by Gilboa and Schmeidler [26] examines case based decision making, which should be of interest to researchers in qualitative decision theory. 22 Although researchers in artificial intelligence (and to some extent statisticians) have examined and used various qualitative notions of knowledge, belief (e.g. 12, 29, 8] and ....

I. Gilboa and D. Schmeidler. Case-based decision theory. The Quarterly Journal of Economics, 110:605--639, 1995.

....set inclusion, such that g( 0 and g(S) 1. Dually, the optimistic qualitative utility is the possibility of the same fuzzy event: u (f) Pi(F ) corresponding to the fuzzy integral u (f) sup ff2[0;1] min(ff; Pi(F ff ) 4. 2 Towards case based decision Recently, Gilboa and Schmeidler [7] have advocated an approach to decision, based on the notion of similarity. In this approach, the decision maker uses a memoryM of cases, viewed as triples (s; a; r) where s is a state of the world, a an action, and r its result in state s. Let S be a non negative function which estimates the ....

....s 0 , he chooses an action a which maximizes the following criterion, counterpart of classical expected utility: U s0 ;M (a) X (s;a;r)2M S(s 0 ; s) Delta u(r) where u is a non negative utility function. Note that contrary to classical expected utility, P (s;a;r)2M S(s 0 ; s) 6= 1. In [7], an axiomatic justification of this criterion is given. The intuitive interpretation of U is to give preference to acts which in similar situations led to results with a high utility. However, with this approach an act which gives a low, but non zero, utility in many similar cases can be ....

I. Gilboa, D. Schmeidler, Case-based decision theory. The Quarterly Journal of Economics, Aug. 1995, 607639.

....with a learning module. Using this module, when a new case is recognized, this case and its consequences, as well as the results of the subsequent decision are recorded, thereby enriching the case memory (Kolodner, 1983) This kind of reasoning by similarity has been recognized for a long time, Gilboa and Schmeidler (1992) quote Hume (1748) and Keynes (1921) It is clear that people draw, by analogy (real or alleged) many conclusions from their experience . I think that subjective probabilities are also very sensitive to analogical reasoning and could be deduced from cases. Up to now, case based reasoning did not ....

....reasoning and could be deduced from cases. Up to now, case based reasoning did not worry too much about future and preferences and has appeared to be appropriate as a substitute for function j (Section 2) But recently some researchers have tried to introduced preferences in case based reasoning (Gilboa and Schmeidler, 1992, 1993) Let us briefly outline their ideas. They try to reconcile case based reasoning and decision theory. In their framework, a case is a triplet (q, a,r) where q is a problem, a is an action and r a result (outcome) Given a similarity real function s(p,q) on the couples (p, q) of problems ....

Gilboa I. and Schmeidler D., 1992, "Case-based Decision theory", Working Paper, Northwestern University.

....have appeared that try to provide a similar foundation for the decision theory of agents with limited rationality. Some of these attempts explicitly formulate, and discuss the idea that we have used here of procedures . We may try here to quote a few, like [1] 2] 6] 8] 9] 10] 11] [14], 15] 26] 27] 28] but 15 the literature is very large, and growing. Some of these contributions explicitly examine criteria for a sound denition of reasonable procedure . Finally, we are not arguing here that we should maintain the assumption of fully rational agents in all cases. ....

Gilboa, I. And Schmeidler, D., (1996), \Case-Based Decision Theory" Quarterly Journal of Economics, 110, 605-639. 24

....but used a stronger monotonicity condition plus continuity. Trockel [42] and Candeal Indurin [8] present results without monotonicity for the preference relation or the representing linear functional. The additivity axiom was also central in early axiomatizations of case based decision theory [19, 20]. The mathematics is related to invariance of preference with respect to a mixing operation ( 16] 45] which similarly leads to linear representations. In Theorem 2, we did not seek for maximal mathematical generality. The purpose of the theorem is to present de Finetti s book making principle ....

Gilboa, Itzhak &David Schmeidler (1995), "Case-Based Decision Theory," Quarterly Journal of Economics 110, 605--639.

....recent use of Bayes networks to specify the notion of relevance of a document to a topic or a query [TC91] In this domain, the notion of retrieving a relevant context or a document is related to our work. Recent ground breaking work in economics introduced the notion of case based decision theory [GS94], where the utility of an action in a particular state is computed by using a kernel density estimation technique over a set of stored memories. Some very recent work in statistics generalizes traditional nearest neighbor learning with adaptive neighborhood techniques. There the issue is finding ....

Z. Gilboa and D. Schmeidler. Case-based decision theory. Technical report, Nortwestern University, 1994.

....is done in order to avoid biasing the similarity metric in favor of any particular feature. 4.2 Choosing a Coordination Strategy COLLAGE chooses a coordination strategy based on how the set of available strategies performed in similar past cases. We adopt the notation from Gilboa and Schmeidler[13] 3 . Each case c is triplet hp; a; ri 2 C i C i P Theta A Theta R where p 2 P and P is the set of situations representing abstract characterization of coordination problems, a 2 A and A is the set of coordination choices available, r 2 R and R is the set of results from running the ....

....work on learning coordination[24] relied on a weak task environment generator where the task structures were generated randomly. The experimenter was limited to setting certain numerical parameters like mean of the task structure depth or mean and variance of the number 3 Gilboa and Schmeidler[13] describe case based decision theory as a normative theory of human behavior during decision making. Even though, we adopt their notation, there are crucial differences in the motivations and structure of the two works. Gilboa and Schmeidler are primary concerned with a descriptive theory of human ....

Itzhak Gilboa and David Schmeidler. Case-based Decision Theory. The Quaterly Journal of Economics, pages 605--639, August 1995.

....we find a recent use of Bayes networks to specify the notion of relevance of a document to a topic or a query [TC91] In this domain, the notion of retrieving a relevant context or a document is related to our work. Recent papers in economics introduced the notion of case based decision theory [GS94], where the utility of an action in a particular state is computed by using a kernel density estimation technique over a set of stored memories. Some very recent work in statistics generalizes traditional nearest neighbor learning with adaptive neighborhood techniques. There the issue is finding ....

Z. Gilboa and D. Schmeidler. Case-based decision theory. Technical report, Northwestern University, 1994.

....performer. Hence, hand coding the strategies by a designer is not a practical alternative. 4.2 Choosing a Coordination Strategy COLLAGE chooses a coordination strategy based on how the set of available strategies performed in similar past cases. We adopt the notation from Gilboa and Schmeidler[Gilboa Schmeidler, 1995] . Each case c is triplet hp; a; ri 2 C i C i P Theta A Theta R where p 2 P and P is the set of situations representing abstract characterization of coordination problems, a 2 A and A is the set of coordination choices available, r 2 R and R is the set of results from running the ....

Gilboa, I., and Schmeidler, D. 1995. Case-based Decision Theory. The Quaterly Journal of Economics 605--639.

....where each component is the average of all the corresponding local situation vector components. Choosing a Coordination Strategy COLLAGE chooses a coordination strategy based on how the set of available strategies performed in similar past cases. We adopt the notation from Gilboa and Schmeidler(Gilboa Schmeidler 1995). Each case c is triplet hp; a; ri 2 C i C i P Theta A Theta R where p 2 P and P is the set of situations representing abstract characterization of coordination problems, a 2 A and A is the set of coordination choices available, r 2 R and R is the set of results from running the ....

Gilboa, I., and Schmeidler, D. 1995. Case-based Decision Theory. The Quaterly Journal of Economics 605--639.

....of case based reasoning for solving configuration problems. The case based reasoning paradigm is used in connection with decision theoretic ideas, realized by the method of case based decision theory (CBDT) This method, which has been developed recently with economic applications in mind [8, 9, 10], seems to provide an interesting basis for the experience based solution of problems in combinatorial optimization. In this approach, learning principally corresponds to memorizing previously solved configuration problems, i.e. building up a case base which consists of a set of configuration ....

....for solving RBC problems. For this purpose, we try to make use of the case based reasoning paradigm. However, we will use this approach only in so far as it is a part of the decision theoretic framework called case based decision theory (CBDT) which was recently proposed by Gilboa and Schmeidler [8, 9, 10]. That is, our basic idea is to interprete the optimization problem associated with RBC in the context of decision theory. In this framework, the derivation of an optimal solution is equivalent to finding (locally) optimal decisions in the solution process. The learning of optimal decisions is ....

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I. Gilboa and D. Schmeidler. Case-based decision theory. Quarterly Journal of Economics, 110(4):605--639, 1995.

....recent use of Bayes networks to specify the notion of relevance of a document to a topic or a query [TC91] In this domain, the notion of retrieving a relevant context or a document is related to our work. Recent ground breaking work in economics introduced the notion of case based decision theory [GS94], where the utility of an action in a particular state is computed by using a kernel density estimation technique over a set of stored memories. Some very recent work in statistics generalizes traditional nearest neighbor learning with adaptive neighborhood techniques. There the issue is finding ....

Z. Gilboa and D. Schmeidler. Case-based decision theory. Technical report, Nortwestern University, 1994.

....may provide a useful alternative theory of rationality for resource limited agents. 1 Introduction The concepts of probability and utility are well established and have been used extensively in connection with game theory or decision making under uncertainty. Recently, Gilboa and Schmeidler [3] have proposed a decision theory in which the concept of similarity (next to utility) plays an important role. Moreover, during the last years this concept has also become a focus of attention within other research fields. Considerable research efforts have been made in this direction in ....

....proportional to the similarity of the situations S and S k . This definition, which realizes some kind of interpolative reasoning, is closely related to the definition of case based utility in the approach of Gilboa 1 The fact that P is indeed a probability measure is obvious. and Schmeidler [3]. Their case based decision theory (Cbdt) assumes a set M of triples (q; a; r) where q is a problem situation, a is an act (a decision) and r is the consequence resulting from that act in the corresponding situation. Faced with a new problem situation p a decision maker estimates the utility ....

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I. Gilboa and D. Schmeidler. Case-based decision theory. Quarterly Journal of Economics, 110(4):605--639, 1995.

....be briefly investigated in Section 2, where strong dependencies expressing that the value of X (fuzzily) determines the value of Y, are contrasted with weak dependencies stating only that if the X values are similar, it is possible that the Y values are similar. Besides, Gilboa and Schmeidler [10] have recently proposed an axiomatized approach to casebased decision, where a similarity based counterpart of expected utility is justified. Interestingly enough, the decision procedure they advocate looks somewhat similar to Sugeno and Nishida [15] approach to fuzzy rule based control, where a ....

....min(S(s,s 0 ) T(t,t ) 3) 3 Gilboa and Schmeidler s Approach Computing the result of a case based inference is not only a matter of retrieving similar relevant cases, even if no adaptation is to be performed, as shown by the case based decision paradigm. Recently, Gilboa and Schmeidler [10] have advocated a similarity based approach to decision where a case is described as a triple (problem, act, result) and where a decision maker s nonnegative utility function u assigns a numerical value u(r) to a result r. When faced with a new situation s 0 , the decision maker is supposed to ....

[Article contains additional citation context not shown here]

Gilboa I. and Schmeidler D., Case-based decision theory, The Quarterly J. of Economics, August 1995, pp. 607-639.

....in order to avoid biasing the similarity metric in favor of any particular feature. 5.5.3 Choosing a Coordination Strategy COLLAGE chooses a coordination strategy based on how the set of available strategies performed in similar past cases. We shall adopt the notation from Gilboa and Schmeidler[Gilboa and Schmeidler, 1995] 5 . Each case c is triplet hp; a; ri 2 C i where p 2 P and P is the set of situations representing abstract characterization of coordination problems, a 2 A and A is the set of coordination choices available, r 2 R and R is the set of results from running a coordination strategy. C i P ....

....are made based on similar past cases. Outcomes decide the desirability of the strategies. We define a similarity function and a utility functions as follows: s : P 2 [0; 1] u : R In the experiments presented later, we use the Euclidean metric for similarity. 5 Gilboa and Schmeidler[Gilboa and Schmeidler, 1995] describe case based decision theory as a normative theory of human behavior during decision making. Even though, we adopt their notation, there are crucial differences in the motivations and structure of the two works. Gilboa and Schmeidler are primary concerned with a descriptive theory of human ....

Gilboa, I. and Schmeidler, D. Case-based Decision Theory. The Quaterly Journal of Economics, pages 605--639, August 1995.

.... metaphors, or images, in short, models that should not be expected to provide a complete and accurate description of reality. We will therefore allow ourselves the idealizations according to which cases can be known, and can be observed independently of rules or theories. Gilboa and Schmeidler CB Knowledge and Induction 10 4.2 Case Based Decision Theory One may agree that only cases can be known, and yet question the appropriateness of the CBDT model. Indeed, many other representations of cases are possible, and one may suggest many alternatives to the CBDT functionals described above. We now turn to justify the ....

.... simplicity. Indeed, it merely translates the choice of a complexity measure to the choice of the appropriate programming language. By contrast, Hume argues that from similar causes we expect similar effects. That is, that the process of implicit induction, or extrapolation, is based on the Gilboa and Schmeidler CB Knowledge and Induction 20 notion of similarity, rather than on simplicity. Needless to say, similarity is just as subjective as simplicity, or as the appropriate language. If we take simplicism as a formulation of Wittgenstein s view, and CBDT as a formulation of Hume s, we have a formal basis on which the two ....

Gilboa, I. and D. Schmeidler (1995a), "Case-Based Decision Theory," The Quarterly Journal of Economics, 110, 605-639.

....1 can also have other interpretations. In particular, the objects to be ranked may be possible acts, with the interpretation of ranking as preferences. Gilboa and Schmeidler (1999b) discuss this interpretation at length, comparing it to expected utility theory and to case based decision theory (Gilboa and Schmeidler (1995,1999a) Gilboa, Schmeidler, and Wakker (1999) apply this theorem, as well as an alternative approach, to axiomatize a theory of case based decisions in which both the similarity function between 21 cases and the utility function of outcomes are derived from preferences. This model generalizes ....

Gilboa, I. and D. Schmeidler (1995), "Case-Based Decision Theory", Quarterly Journal of Economics, 110: 605-639.

....relations over acts (rather than plausibility relations over eventualities) even if states of the world cannot be formulated in an intuitive way. Ranking acts according to f = SI may be viewed as a generalization of expected utility theory (EUT) and of case based decision theory (CBDT) of Gilboa and Schmeidler (1995,1997,1999a) By identifying cases with states and setting V to be the identity matrix, one may represent an expected utility maximizer as a case based f maximizer who recalls a case for each conceivable state, and whose probability judgments are based on empirical frequencies. Thus f maximization ....

Gilboa, I. and D. Schmeidler (1995), "Case-Based Decision Theory", Quarterly Journal of Economics, 110: 605-639.

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Gilboa, I., Schmeidler, D.: Case-based decision theory. Quarterly Journal of Economics 110 (1995) 605--639

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Gilboa, I. and D. Schmeidler. 1995. Case-Based Decision Theory. The Quarterly Journal of Economics, 110(3):605--639.

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I. Gilboa and D. Schmeidler, Case-based decision theory, mimeo, Kellogg School of Management, Northwestern University (1992).

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Gilboa I. and Schmeidler D., 1995, Case-Based Decision Theory, Quaterly Journal of Economics 110, 605--639.

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Gilboa, I. and Schmeidler, D. (1992): \Case-Based Decision Theory", DP Northwestern University.

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Gilboa, I., Schmeidler, D., 1995, Case-Based Decision Theory, Quarterly Journal of Economics, Vol. 110, 605-640.

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