Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches

Conceptualising uncertainty in environmental decision-making: The example of the EU Water Framework Directive

The question of how to deal with uncertainty in environmental decision-making is cur-rently attracting considerable attention on the part of scientists as well as of politicians and those involved in government administration. The existence of uncertainty becomes particularly apparent in the field of environmental policy because environmental prob-lems are regarded as highly complex and long-term and because far-reaching changes have to be taken into account; moreover, the knowledge available to practitioners and policy makers alike is often fragmentary and not systemised. One key issue arising from this is the challenge to develop scientific decision support methods that are capable of dealing with uncertainty in a systematic and differentiated way, integrating scientific and practical knowledge. This paper introduces a conceptual framework for perceiving and describing uncertainty in environmental decision-making. It is argued that perceiv-ing and describing uncertainty is an important prerequisite for deciding and acting under uncertainty. The conceptual framework consists of a general definition of uncertainty along with five complementary perspectives on the phenomenon, each highlighting one specific aspect of it. By using the conceptual framework, decision-makers are able to re-flect on their knowledge base with regard to its completeness and reliability and to gain a broad picture of uncertainty from various standpoints. The theoretical ideas presented here are based on two empirical studies looking at how uncertainty is dealt with in the implementation process of the EU Water Framework Directive (WFD). The rather ab-stract differentiations are illustrated by a number of examples in the form of interview statements and excerpts from the WFD and the WFD guidance documents Impress, Wateco und Proclan. --uncertainty,probability,lack of knowledge,pure ignorance,environ-mental decision-making,EU Water Framework Directive (WFD)

Beyond Earthquakes: The New Directions of Expected Utility Theory

Over the past two decades or so, an enormous amount of work has been done to improve the Expected Utility model. Two areas have attracted major attention: the possibility of describing unforeseen contingencies and the need to accommodate the kind of behavior referred to in Ellsberg’s paradox. This essay surveys both.

Rational ignorance and the public choice of redistribution

This paper studies the role of citizensÂ’ demand for political information in elections and provides a possible explanation for the poor empirical support encountered by political economy models of income redistribution. It shows that incentives to gather political information may derive from its relevance to private choices. Under quite mild assumptions, the demand for political information is increasing in income. Information affects citizensÂ’ responsiveness to electoral platforms, and vote-seeking political parties should take this into account: as a consequence, redistribution will generally be less than predicted by the median voter theorem. Moreover, in contrast with what most literature seems to take for granted, an increase in inequality will not unambigously increase redistribution. Finally, introducing endogenous information may lead some policy restrictions to have effects quite different from those intended.redistribution, median voter, information, inequality

History, Crucial Choices and Equilibrium

This paper discusses alternative conceptions of time and scrutinises the ideas of crucial choice, determinism and equilibrium. The relevant notion is that of historical time, where time is seen as irreversible, flowing from the irrevocable past to an unknown future, like an arrow. This notion is consistent with the concept of fundamental uncertainty and is at odds with deterministic explanations of reality. The economy is an open, evolving process in which free will, Shacklean genuine choices, Schumpeterian innovative behaviours, and unpredictable, unintended consequences of human actions have an important role to play. Human imagination and crucial decisions preclude the full operation of rigid laws of necessity. In the light of these ideas, the paper also approaches a few suggestions of reconceptualisations of the notion of equilibrium which purport to render the concept more palatableHistorical Time, Crucial Choices, Shackle, Determinism, Equilibrium.

Bayesian Learning for a Class of Priors with Prescribed Marginals

We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a ``weighted maximum likelihood method'' and a ``semi-classical method.'' The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter.Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model