On State Dependent Preferences and Subjective Probabilities

When is there state independence?

“…This opens the question of the degree to which given representations for state-dependent utilities treat "essentially" stateindependent utilities or not: it is perhaps important to distinguish the state-dependent utility theorems which can deal with preference relations which are not essentially monotonic from those which cannot. Most of the results mentioned here, with the possible exception of [Karni et al, 1983, Drèze, 1987, are in the latter category.…”

“…First of all, since the state space is finite, the integral reduces to a sum. Furthermore, since acts can be expressed as mixtures of acts yielding certain lotteries (footnote 2), it is common to consider acts as functions from S × C to the reals satisfying certain conditions [Karni et al, 1983, Karni and Mongin, 2000, Fishburn, 1970. It is thus possible to recover a representation of the following, standard, form from the representation given in the text: for any acts f, g, f g iff…”

“…There has been much discussion of representations of preferences with statedependent utilities [Karni et al, 1983, Karni and Schmeidler, 1993, Karni, 1993, Karni and Mongin, 2000, Drèze, 1987, Schervish et al, 1990. In several of these discussions, it has been noted that, by redefining which acts count as "constant", one will transform a state-independent representation into a state-dependent one, and inversely, transform a state-dependent representation into a state-independent one.…”

Three Analyses of Sour Grapes

“…The sour grape story involves two situations: the situation before the fox's first attempt at getting the grapes (which shall be called "the first situation"); the situation after this attempt, and in which he takes his decision to try again or to give in (the "second situation"). 10 See, for example, Karni et al (1983); Karni and Mongin (2000); Drèze (1987). 11 A disadvantage of this generality is the difficulty in comparing utilities involved in decision problems which do not share the same set of states of the world.…”

Risk, ambiguity, and state-preference theory

“…If the decision maker is truly risk neutral with state-independent utility for money, her risk neutral probabilities can be directly interpreted as subjective probabilities, which is the de…nition proposed by de Finetti (1937,1974). But if she has subjective expected utility preferences and is risk averse, her risk neutral probabilities must be interpreted instead as products of subjective probabilities and relative marginal utilities for money, where the latter may depend on unobservable background risk such as pre-existing …nancial and psychological stakes in events as well as on intrinsic state-dependence of utility (Karni et al 1983, Karni 1985, Nau 2001b. It is therefore generally impossible to uniquely separate probabilities from utilities based on observations of the decision maker's preferences among bets (or any other concrete acts, for that matter), and if she has non-expected-utility preferencesin particular, preferences that exhibit aversion to ambiguity-then her beliefs may not be representable by subjective probabilities at all, even in principle.…”