Abstract
Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.
Highlights
Methods and tools for analyzing and evaluating decision problems under risk have been of great interest for a long time
To illustrate how second-order risk constraints contrast with first-order models and how SORC can show distinctions that are not possible to reveal with first-order models such as contraction we show two examples
One criticism is that the classical notion of a utility function cannot cover some quite natural risk behavior, such as not accepting an alternative independently of its expected utility because one or more consequences are too severe regardless of there existing consequences with high utilities and high probabilities to occur, resulting in a beneficial expected utility
Summary
Methods and tools for analyzing and evaluating decision problems under risk have been of great interest for a long time. The elicitation of risk attitudes from human decision-makers is error prone and the result is highly dependent on the formats and methods used, see, e.g., [12,13] for overviews of the state-of-the-art in elicitation This problem is even more evident when the decision situation involves catastrophic outcomes [14]. Severe-consequence domains have been suggested [16,17] This approach puts emphasis on the tails of probability distributions over different kinds of values at risk in the case of a catastrophic scenario; still not discarding the unconditional probability of an extreme event occurring, but treating both the conditional and unconditional expected values as decision objectives. The last section before the conclusion presents how risk constraints can be realized in a second-order framework for evaluating decisions under risk together with a small example using two approaches to cope with imprecise information when evaluating decision alternatives with risk constraints
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