We introduce a general model of static choice under uncertainty, which is arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the popular non-expected utility models existing in the literature are special cases of it. To prove the interest of such a general model, we show that it has a simple and natural axiomatization, and that it can be used to generalize several well known results on the characterization of risk aversion. These generalizations are of some independent interest, as they show that some traditional results for preferences which satisfy the subjective expected utility model can be formulated only in terms of binary acts. As the separation of utility and beliefs here achieved allows to identify and remove aspects of risk attitude from the decision maker's behavior, the model can also be very helpful in the characterization of a notion of ambiguity aversion (see Ambiguity Made Precise).
The theory of subjective expected utility (SEU) has been recently extended to allow ambiguity to matter for choice. However, a general notion of ambiguity aversion, one which can be applied to a large subset of preference relations, is still missing. Using a preference model which encompasses some of the most popular models in the literature, we propose a notion by building on a notion of comparative ambiguity aversion. A difficulty in developing the latter is the need to discriminate between differences in ambiguity and risk attitude. The solution we offer, while possibly not complete, is quite general, as it only requires a richness condition on the set of payoffs. Employing the comparative notion, we suggest to call `ambiguity averse' a preference relation which is `more ambiguity averse than' a SEU preference with similar risk attitude. We show that ambiguity aversion in this broad sense has a simple characterization, especially for two of the most popular models in the literature. We next build on these ideas to provide a definition of `unambiguous' act and event. We show that for preferences which are ambiguity averse or loving, the sets of these acts and events have a simple and easily checked characterization. As an illustration, we consider the classical Ellsberg 3-color urn problem and find that the notions developed in the paper provide intuitive answers.
We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs.
We show that range convexity of beliefs, a `technical' condition that appears naturally in axiomatizations of preferences in a Savage-like framework, imposes some unexpected restrictions when modelling ambiguity averse preferences. That is, when it is added to a mild condition, range convexity makes the preferences collapse to subjective expected utility as soon as they satisfy structural conditions that are typically used to characterize ambiguity aversion.
In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the decision problem is too coarse, as for instance when there might be unforeseen contingencies. I make a ``bounded rationality'' assumption on the way the DM deals with this difficulty, and then I show that imposing standard subjective expected utility axioms on her preferences only implies that they can be represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. However, the axioms do have strong implications for how the DM copes with the type of ignorance described above. Finally, I show that some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently).
We address the so-called ``roll-off'' phenomenon: Selective abstention in multiple elections. We present and discuss a novel model of decision making by voters that explains this as a result of differences in quality and quantity of information that the voters have about each election. In doing so we use a spatial model that differs from the Euclidean one, and is more naturally applied to modelling differences in information.