Abstract
A set of decisions or a person’s preference relation over actions is coherent only if there exists a probability function over the set of events as well as a subjective utility function over the set of consequences, such that the (subjective) expected utility of the preferred decision is, in each case, higher than that of the non-preferred decision.1
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Reference
See Jeffrey (1965a), p. 533 f
There are many good introductions to rational decision theory, especially to the theory of decisions under risk. See e. g. Chernoff/Moses (1959), Luce/Suppes (1963), Raiffa (1978).
See especially the theories of Savage (1954), Jeffrey (1967) and Fishburn (1964, 1966, 1970, 1972)
For a detailed analysis of different models of decisions see Spohn (1978) and also Stegmüller (1973).
Savage (1954), p. 9. Strictly speaken, however, we have no assumptions about subjective probabilities and about subjective desirabilities of descriptions but rather of the described.
Jeffrey (1967), p. 208.
E is a Boolean algebra. See Jehle (1974).
A decision situation in the narrow sense comprises situations under risk and certainty without interaction.
We assume all sets to be finite and nonempty.
See Jeffrey (1967), p. 80.
See Spohn (1978), p. 77 ff.
More precisely: the subsets of c being singletons.
Analogously, we have in all decision models not a direct but a derived valuation of actions (which is relative to the valuation of the consequences and the probabilities).
Consequences are not ‘states of the person’ or descriptions under characteristics which ι takes to be relevant for his/her utility.
Hereby, we are satisfying Spohn’s demand not to extend the definition of the probability function pι to alternative actions (Σ ι), see Spohn (1978), pp. 72–78.
If one knows the subset of Pot(Ξ) over which ρι can reasonably be defined, one is still left with the choice to choose from different partitions of Pot(Ξ) resp. c, the elements of which belong to the set over which ρι is defined. Naturally, not every subset of Pot(Ξ) allows for such a partition, but we can demand every set over which a subjective probability function is defined to have this property.
To this rethoric question, there is even another answer apart from ‘nobody’, namely ‘Jeffrey’ — cf. the quoted passage above, in which states are identified with complete novels. We should not accept this identification, however, since with it language would be assumed to have to strong a function in ‘making up the world’.
Of course, a person can describe her own actions propositionally; however, in our model they are not an element of the set of events, but functions from U to C, by which we avoid the problem of singling out specific types of propositions from the set over which the subjective probability function is defined.
See Debreu (1959), pp. 55–59.
Sometimes, these two axioms are called ‘basic utility axioms’, see Harsanyi (1979).
A lottery is a chance experiment with known probabilities and outcomes associated to the probabilties: (math)
See Brandt (1979), ch. VI, and Stegmüller (1977).
For this issue, see Gärdenfors (1979).
Coherent behaviour does not have to be rational, but one can expect an adequate concept of consistency to support the implication that rational behaviour is consistent. It is unclear as to whether the Bayesian concept of consistency allows for this as Allais’ critique of Bayesianism has shown. See Allais (1953) and for the subsequent discussion Allais/Hagen (1979). The departing point is that persons systematically violated the Bayesian axioms of consistency when taking part in experiments (see also Schneeweiß (1967), p. 79).
One can see that metatheoretical questions of probability theory bear upon the question which criterion for situations under ignorance one accepts, since a subjectivist (w. r. t. probabilities) probably would reject the proposal.
This is also called Wald-criterion, see Wald (1950).
See Savage (1951).
See Luce/Raiffa (1957), S. 282 ff.
See Milnor (1954). Not all of the ten metacriteria for rational decision listed by Milnor can claim a selective function, the remaining rather serve for characterizing competing criteria.
Other then Gärdenfors (see Gärdenfors 1979), we also assume intervals of probability conditioned by actions.
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© 1997 Springer Science+Business Media Dordrecht
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Nida-Rümelin, J. (1997). Formal Economic Rationality. In: Economic Rationality and Practical Reason. Theory and Decision Library, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8814-0_5
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DOI: https://doi.org/10.1007/978-94-015-8814-0_5
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