The Opinion Pool

Stone, M.

doi:10.1214/aoms/1177704873

Cited by 375 publications

(206 citation statements)

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“…The best-known example is a linear pooling function, which goes back to Stone (1961) or even Laplace. 2 Here, each opinion pro…le (P 1 ; :::; P n ) in the domain P n is mapped to the collective probability function satisfying P P 1 ;:::;Pn (A) = w 1 P 1 (A) + + w n P n (A) for every event A , where w 1 ; :::; w n are …xed non-negative weights with sum-total 1.…”

Section: The Problem Of Probabilistic Opinion Poolingmentioning

confidence: 99%

Probabilistic Opinion Pooling

Dietrich

List

2017

Oxford Handbooks Online

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Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This chapter is a review of several proposed solutions to this problem, focusing on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). Axiomatic characterizations of each class of pooling functions are presented (most characterizations are classic results, but one is new), with the argument that linear pooling can be justified “procedurally” but not “epistemically”, while the other two pooling methods can be justified “epistemically”. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. In conclusion a number of other pooling methods are mentioned.

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Section: The Problem Of Probabilistic Opinion Poolingmentioning

confidence: 99%

Probabilistic Opinion Pooling

Dietrich

List

2017

Oxford Handbooks Online

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“…This rule for aggregation of probabilistic assessments has been dubbed linear opinion pool by Stone [37], and is attributed to Laplace (see [2,29,16], for a survey).…”

Section: The Bayesian Casementioning

confidence: 99%

Aggregation of multiple prior opinions

Crès

Gilboa

Vieille

2011

Journal of Economic Theory

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Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker's utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker's set of priors is precisely all the weighted-averages of priors, where an expert's prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker's valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts' valuations.

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“…The state of the agents is a continuous variable, representing an opinion, that evolves according to rules tending to homogenize the system. The conditions to reach consensus in this model were analyzed in previous works [4,5], but several interesting properties were not studied. In particular, we analyze the transient state during which the formation of the collective opinion takes place, as well as the relevance of dynamical time scales in the formation of minorities.…”

Section: Introductionmentioning

confidence: 99%

Minorities in a model for opinion formation

2004

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We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity 7, 2, 55 (2002)]. The convergent opinion adjustment process takes place as a result of random binary encounters whenever the difference between agents' opinions is below a given threshold. The inhomogeneity in the dynamics gives rise to a complex steady state structure, which is also highly dependent on the threshold and on the convergence parameter of the model.

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The Opinion Pool

Cited by 375 publications

References 0 publications

Probabilistic Opinion Pooling

Probabilistic Opinion Pooling

Aggregation of multiple prior opinions

Minorities in a model for opinion formation

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