Management Science
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic inference and influence diagrams
Operations Research
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
Management Science
The topological fusion of Bayes nets
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Aggregating point estimates: a flexible modeling approach
Management Science
Methods for combining experts' probability assessments
Neural Computation
Journal of the ACM (JACM)
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Compact Securities Markets for Pareto Optimal Reallocation of Risk
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Directed reduction algorithms and decomposable graphs
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Graphical representations of consensus belief
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Representing aggregate belief through the competitive equilibrium of a securities market
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Pricing combinatorial markets for tournaments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Average and Majority Gates: Combining Information by Means of Bayesian Networks
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Decision Analysis
Managing uncertainty in group recommending processes
User Modeling and User-Adapted Interaction
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We investigate the practical value of using graphical models to aid in two fundamental problems of group coordination: (1) belief aggregation and (2) risk sharing. We identify restrictive conditions under which graphical models can be useful in both settings. We show that the output of the logarithmic opinion pool (LogOP) can be represented as a Markov network (MN) or a decomposable Bayesian network (BN), and give an algorithm for doing so. We show that a securities market structured like a decomposable BN can support optimal risk sharing, if all agents have exponential utility and all of their Markov independencies coincide with the market structure. On the other hand, most of our results are negative, taking the form of impossibility theorems. We show that no belief aggregation function can maintain all independencies representable in a BN. Neither can an aggregation computation be decomposed into local computations on graph subsets. We show that computing query outputs of LogOP or the linear opinion pool (LinOP) is NP-hard. Except in fairly restrictive settings, structuring securities markets according to unanimously agreed upon independencies may be of no help in supporting optimal risk sharing because agents' behavioral independencies change as they engage in securities trade.