Probabilistic Evaluation of Preference Aggregation Functions: A Statistical Approach in Social Choice Theory

A statistical criterion for evaluating the appropriateness of preference aggregation functions for a fixed group of persons is introduced. Specifically, we propose a method comparing aggregation procedures by relying on probabilistic information on the homogeneity structure of the group members’ preferences. For utilizing the available information, we give a minimal axiomatization as well as a proposal for measuring homogeneity and discuss related work. Based on our measure, the group specific probability governing the constitution of preference profiles is approximated, either relying on maximum entropy or imprecise probabilities. Finally, we investigate our framework by comparing aggregation rules in a small study

Aggregation of expert opinions and uncertainty theories

National audienceThe problem of expert opinions representation and aggregation has long been adressed in the only framework of probability theory. Nevertheless, recent years have witnessed many proposals in other uncertainty theories (possibility theory, evidence theory, imprecise probabilities). This paper casts the problem of aggregating expert opinions in a common underlying framework and shows how uncertainty theories fit into this framework. Differences between theories are then emphasized and discussed

The Effect of Communicating Ambiguous Risk Information on Choice

Decision makers are frequently confronted with ambiguous risk information about activities with potential hazards. This may be a result of conflicting risk estimates from multiple sources or ambiguous risk information from a single source. The paper considers processing ambiguous risk information and its effect on the behavior of a decision maker with a-maximin expected utility preferences. The effect of imprecise risk information on behavior is related to the content of information, the decision maker’s trust in different sources of information, and his or her aversion to ambiguity.a-Maximin Expected Utility, aggregation of expert opinions, ambiguity, Knightian uncertainty, risk communication, trust in information source, Risk and Uncertainty,

Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling

Generalized basic probability assignments

Dempster-Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering SETS of basic probability assignments, an appealing constructive approach to general interval probability (general imprecise probabilities) is achieved, which allows for a very flexible modelling of uncertain knowledge

Dilating and contracting arbitrarily

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a precise state arbitrarily

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