Upper and Lower Probabilities Induced by a Multivalued Mapping

Dempster, A. P.

doi:10.1007/978-3-540-44792-4_3

Cited by 1,728 publications

(890 citation statements)

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“…some of McFadden's generalized extreme value models-see Small, 1986) also belong to the Markov transition class. Wagner's (1989) work on consensus for belief functions (Dempster, 1967;Sharer, 1976), and his suggestions for further work on that problem, have close relations to the above formulation.…”

Section: P(x : E) >~ P(x : F) Whenever E _c F Nonetheless Further Wmentioning

confidence: 99%

Aggregation theorems and multidimensional stochastic choice models

Marley

1991

Theor Decis

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In many choice situations, the options are multidimensional. Numerous probabilistic models have been developed for such choices between multidimensional options and for the parallel choices determined by one or more components of such options. In this paper, it is assumed that a functional relation exists between the choice probabilities over the multidimensional options and the choice probabilities over the associated component unidimensional options. It is shown that if that function satisfies a marginalization property then it is essentially an arithmetic mean, and if the function satisfies a likelihood independence property then it is a weighted geometric mean. The results are related to those on the combination of expert opinion, and various probabilistic models in the choice literature are shown to have the geometric mean form.

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Section: P(x : E) >~ P(x : F) Whenever E _c F Nonetheless Further Wmentioning

confidence: 99%

Aggregation theorems and multidimensional stochastic choice models

Marley

1991

Theor Decis

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“…Dempster (1967) showed that we could generate upper and lower expected utilities from upper and lower probabilities that are linked to a credibifity measure for the first and to aplausibility measure for the second. Those measures are particular cases of the Shafer's belief functions.…”

Section: The New Measures and Standard Modelsmentioning

confidence: 99%

“…At the same time, many theoreticians (e.g., Dempster, 1967;Luce, 1968;Sugeno, 1972;Suppes, 1974;Shafer, 1976;Nguyen, 1978;Small, 1987;Cohen and Jaffray, 1980;Jaffray, 1988;Thisse and de Palma, 1989) seem to have been searching for a new way of modeling cognitive 1 rationality and thus for a theory of judgments under uncertainty out of the standard model of probability.…”

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confidence: 99%

Cognitive rationality and alternative belief measures

Billot

1991

J Risk Uncertainty

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In this article, we first examine the various criticisms of the probabilistic model. Then we introduce capacities in order to show that if a probability measure corresponds to anesthetizing the belief of the agent's knowledge, it is then possible to suggest another type of rationality--namely, being able to describe a wise and a rash behavior when facing risk--and therefore another model of belief under uncertainty. While trying to specify various alternative measures, possibility, necessity, and measures resulting from a triangular norm or from a triangular conorm, we finally try to define the field of application of the probabilistic model as well as a sign of the rationality choice: constraint of mass-unity for traditional rationality, and constraint of duality for the one we present.During the past 20 years, it seems that progress in computer science and artificial intelligence has generated a new requirement, namely, a theory of belief in uncertainty outside the probabilistic framework (see Buchanan and Shortliffe, 1975;Zadeh, 1975;H6hle, 1982;Simon, 1978). At the same time, many theoreticians (e.g., DempsterThisse and de Palma, 1989) seem to have been searching for a new way of modeling cognitive 1 rationality and thus for a theory of judgments under uncertainty out of the standard model of probability. (who introduce bounded rationality with a kind of decision cost inside the theory of noncooperative games with finite automata), the Simon's concept of bounded rationality on the one hand and the new criticisms of the expected utiltity model on the other hand (see Loomes and Sugden (1982) with their regret theory, and Kahneman and Tversky (1979) with their prospects theory) show us the existence of a latent controversy illustrating the theoreticians' difficulty in using standard models (see also Bell

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“…Among statisticians, the main support for this way of representing imprecise or incomplete opinion comes from. Good (1950Good ( , 1962, Smith (1961), Dempster (1967, 1968), and Shafer (1976. In practice, the business of reasoning in terms of a variable, r or 'est', that satisfies certain constraints, is widespread -but with an unsatisfactory rationale, according to which one is reasoning about an unknown, definite function, which the variable denotes.…”

Section: Solution or Evasion?mentioning

confidence: 99%

Probabilism and induction

Jeffrey

1986

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Upper and Lower Probabilities Induced by a Multivalued Mapping

Cited by 1,728 publications

References 4 publications

Aggregation theorems and multidimensional stochastic choice models

Aggregation theorems and multidimensional stochastic choice models

Cognitive rationality and alternative belief measures

Probabilism and induction

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