40 research outputs found
Expected multi-utility representations of preferences over lotteries
Let be a binary relation on the set of simple lotteries over a
countable outcome set . We provide necessary and sufficient conditions on
to guarantee the existence of a set of von Neumann--Morgenstern
utility functions such that for all simple lotteries . In such case, the set
is essentially unique. Then, we show that the analogue characterization does
not hold if is uncountable. This provides an answer to an open question
posed by Dubra, Maccheroni, and Ok in [J. Econom. Theory~\textbf{115} (2004),
no.~1, 118--133]. Lastly, we show that different continuity requirements on
allow for certain restrictions on the possible choices of the set
of utility functions (e.g., all utility functions are bounded), providing a
wide family of expected multi-utility representations
Objective and Subjective Expected Utility with Incomplete Preferences
This paper extends the expected utility models of decision making under risk and under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multi-prior expected multi-utility representations of preference relation under uncertainty, thereby resolving long standing open questions. The Knightian uncertainty model and expected multi-utility model with complete beliefs are obtained as special cases. In addition, the von Neumann-Morgenstern expected utility model with incomplete preferences is revisited using a "constructive" approach, as opposed to earlier treatments that use convex analysis.
Continuity and completeness of strongly independent preorders
A strongly independent preorder on a possibly infinite dimensional convex set that satisfies two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfies two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided
Risky social choice with approximate interpersonal comparisons of well-being
We develop a model of social choice over lotteries, where people's psychological characteristics are mutable, their preferences may be incomplete, and approximate interpersonal comparisons of well-being are possible. Formally, we suppose individual preferences are described by a von~Neumann-Morgenstern (vNM) preference order on a space of lotteries over psychophysical states; the social planner must construct a vNM preference order on lotteries over social states. First we consider a model when the individual vNM preference order is incomplete (so not all interpersonal comparisons are possible). Then we consider a model where the individual vNM preference order is complete, but unknown to the planner, and thus modeled by a random variable. In both cases, we obtain characterizations of a utilitarian social welfare function
Representation of strongly independent preorders by sets of scalar-valued functions
We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization
Structuring Decisions Under Deep Uncertainty
Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision theorists can both learn from, and contribute to, the growing deep uncertainty decision support literature
Risky social choice with approximate interpersonal comparisons of well-being
We develop a model of social choice over lotteries, where people's psychological characteristics are mutable, their preferences may be incomplete, and approximate interpersonal comparisons of well-being are possible. Formally, we suppose individual preferences are described by a von~Neumann-Morgenstern (vNM) preference order on a space of lotteries over psychophysical states; the social planner must construct a vNM preference order on lotteries over social states. First we consider a model when the individual vNM preference order is incomplete (so not all interpersonal comparisons are possible). Then we consider a model where the individual vNM preference order is complete, but unknown to the planner, and thus modeled by a random variable. In both cases, we obtain characterizations of a utilitarian social welfare function.interpersonal comparisons; social welfare; social choice; utility; utilitarian; von Neumann-Morgenstern; risk
Multi-utility representations of incomplete preferences induced by set-valued risk measures
We establish a variety of numerical representations of preference relations
induced by set-valued risk measures. Because of the general incompleteness of
such preferences, we have to deal with multi-utility representations. We look
for representations that are both parsimonious (the family of representing
functionals is indexed by a tractable set of parameters) and well behaved (the
representing functionals satisfy nice regularity properties with respect to the
structure of the underlying space of alternatives). The key to our results is a
general dual representation of set-valued risk measures that unifies the
existing dual representations in the literature and highlights their link with
duality results for scalar risk measures
Continuous Multi-Utility Representations of Preorders and the Chipman Approach
Chipman contended, in stark contrast to the conventional view, that, utility is not a real
number but a vector, and that it is inherently lexicographic in nature. On the other hand, in recent
years continuous multi-utility representations of a preorder on a topological space, which proved
to be the best kind of continuous representation, have been deeply studied. In this paper, we first
state a general result, which guarantees, for every preordered topological space, the existence of a
lexicographic order-embedding of the Chipman type. Then, we combine the Chipman approach and
the continuous multi-utility approach, by stating a theorem that guarantees, under certain general
conditions, the coexistence of these two kinds of continuous representations