Aggregation of Expert Opinions

Conflicts of interest arise between a decision maker and agents who have information pertinent to the problem because of differences in their preferences over outcomes. We show how the decision maker can extract the information by distorting the decisions that will be taken, and show that only slight distortions will be necessary when agents are "informationally small." We further show that as the number of informed agents becomes large the necessary distortion goes to zero. We argue that the particular mechanisms analyzed are substantially less demanding informationally than those typically employed in implementation and virtual implementation. In particular, the equilibria we analyze are "conditionally" dominant strategy in a precise sense. Further, the mechanisms are immune to manipulation by small groups of agents.Information Aggregation, Mechanism Design, Incomplete Information

Aggregation of Expert Opinions

Conflicts of interest arise between a decision maker and agents who have information pertinent to the problem because of differences in their preferences over outcomes. We show how the decision maker can extract the information by distorting the decisions that will be taken, and show that only slight distortions will be necessary when agents are informationally small. We further show that as the number of informed agents becomes large the necessary distortion goes to zero. We argue that the particular mechanisms analyzed are substantially less demanding informationally than those typically employed in implementation and virtual implementation. In particular, the equilibria we analyze are conditionally dominant strategy in a precise sense. Further, the mechanisms are immune to manipulation by small groups of agents.Information aggregation, Asymmetric information, Cheap talk, Experts

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

Ambiguous Aggregation of Expert Opinions: The Case of Optimal R&D Investment

How should a decision-maker allocate R&D funds when a group of experts provides divergent estimates on a technology's potential effectiveness? To address this question, we propose a simple decision-theoretic framework that takes into account ambiguity over the aggregation of expert opinion and a decision-maker's attitude towards it. In line with the paper's focus on R&D investment, decision variables in our model may affect experts' subjective probability distributions of the future potential of a technology. Using results from convex optimization, we are able to establish a number of analytical results including a closed-form expression of our model's value function, as well as a thorough investigation of its differentiability properties. We apply our framework to original data from a recent expert elicitation survey on solar technology. The analysis suggests that more aggressive investment in solar technology R&D is likely to yield significant dividends even, or rather especially, after taking ambiguous aggregation into account.Aggregation, Ambiguity, R&D, Expert Opinions, Convex/Conic Optimization

Robust weighted aggregation of expert opinions in futures studies

Expert judgments are widespread in many fields, and the way in which they are collected and the procedure by which they are aggregated are considered crucial steps. From a statistical perspective, expert judgments are subjective data and must be gathered and treated as carefully and scientifically as possible. In the elicitation phase, a multitude of experts is preferable to a single expert, and techniques based on anonymity and iterations, such as Delphi, offer many advantages in terms of reducing distortions, which are mainly related to cognitive biases. There are two approaches to the aggregation of the judgments given by a panel of experts, referred to as behavioural (implying an interaction between the experts) and mathematical (involving non-interacting participants and the aggregation of the judgments using a mathematical formula). Both have advantages and disadvantages, and with the mathematical approach, the main problem concerns the subjective choice of an appropriate formula for both normalization and aggregation. We propose a new method for aggregating and processing subjective data collected using the Delphi method, with the aim of obtaining robust rankings of the outputs. This method makes it possible to normalize and aggregate the opinions of a panel of experts, while modelling different sources of uncertainty. We use an uncertainty analysis approach that allows the contemporaneous use of different aggregation and normalization functions, so that the result does not depend on the choice of a specific mathematical formula, thereby solving the problem of choice. Furthermore, we can also model the uncertainty related to the weighting system, which reflects the different expertise of the participants as well as expert opinion accuracy. By combining the Delphi method with the robust ranking procedure, we offer a new protocol covering the elicitation, the aggregation and the processing of subjective data used in the construction of Delphi-based future scenarios. The method is very flexible and can be applied to the aggregation and processing of any subjective judgments, i.e. also those outside the context of futures studies. Finally, we show the validity, reproducibility and potential of the method through its application with regard to the future of Italian families

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,

A comparison between probabilistic and Dempster-Shafer Theory approaches to Model Uncertainty Analysis in the Performance Assessment of Radioactive Waste Repositories

Model uncertainty is a primary source of uncertainty in the assessment of the performance of repositories for the disposal of nuclear wastes, due to the complexity of the system and the large spatial and temporal scales involved. This work considers multiple assumptions on the system behavior and corresponding alternative plausible modeling hypotheses. To characterize the uncertainty in the correctness of the different hypotheses, the opinions of different experts are treated probabilistically or, in alternative, by the belief and plausibility functions of the Dempster-Shafer theory. A comparison is made with reference to a flow model for the evaluation of the hydraulic head distributions present at a radioactive waste repository site. Three experts are assumed available for the evaluation of the uncertainties associated with the hydrogeological properties of the repository and the groundwater flow mechanisms

A new decision making model based on Rank Centrality for GDM with fuzzy preference relations

The work of Enrique Herrera Viedma was supported by the Spanish State Research Agency under Project PID2019-103880RB-I00/AEI/10.13039/501100011033.Preference aggregation in Group Decision Making (GDM) is a substantial problem that has received a lot of research attention. Decision problems involving fuzzy preference relations constitute an important class within GDM. Legacy approaches dealing with the latter type of problems can be classified into indirect approaches, which involve deriving a group preference matrix as an intermediate step, and direct approaches, which deduce a group preference ranking based on individual preference rankings. Although the work on indirect approaches has been extensive in the literature, there is still a scarcity of research dealing with the direct approaches. In this paper we present a direct approach towards aggregating several fuzzy preference relations on a set of alternatives into a single weighted ranking of the alternatives. By mapping the pairwise preferences into transitions probabilities, we are able to derive a preference ranking from the stationary distribution of a stochastic matrix. Interestingly, the ranking of the alternatives obtained with our method corresponds to the optimizer of the Maximum Likelihood Estimation of a particular Bradley-Terry-Luce model. Furthermore, we perform a theoretical sensitivity analysis of the proposed method supported by experimental results and illustrate our approach towards GDM with a concrete numerical example. This work opens avenues for solving GDM problems using elements of probability theory, and thus, provides a sound theoretical fundament as well as plausible statistical interpretation for the aggregation of expert opinions in GDM.Spanish State Research Agency PID2019-103880RB-I00/AEI/10.13039/50110001103