Above are papers related to the following paper: [Paper_ID] Paper #1132857. 	[Title] A Market Framework for Pooling Opinions [Abstract] Consider a group of Bayesians, each with a subjective probability distribution over a set of uncertain events. An opinion pool derives a single consensus distribution over the events, representative of the group as a whole. Several pooling functions have been proposed, each sensible under particular assumptions or measures. Many researchers over many years have failed to form a consensus on which method is best. We propose a market-based pooling procedure, and analyze its properties. Participants bet on securities, each paying off contingent on an uncertain event, so as to maximize their own expected utilities. The consensus probability of each event is defined as the corresponding security's equilibrium price. The market framework provides explicit monetary incentives for participation and honesty, and allows agents to maintain individual rationality and limited privacy. "No arbitrage" arguments ensure that the equilibrium prices form legal probabilities. We show that, when events are disjoint and all participants have exponential utility for money, the market derives the same result as the logarithmic opinion pool; similarly, logarithmic utility for money yields the linear opinion pool. In both cases, we prove that the group's behavior is, to an outside observer, indistinguishable from that of a rational individual, whose beliefs equal the equilibrium prices. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #682508. 	[Title] Representing Aggregate Belief through the Competitive Equilibrium of a Securities Market [Abstract] We consider the problem of belief aggregation: given a group of individual agents with probabilistic beliefs over a set of of uncertain events, formulate a sensible consensus or aggregate probability distribution over these events. Researchers have proposed many aggregation methods, although on the question of which is best the general consensus is that there is no consensus. We develop a market-based approach to this problem, where agents bet on uncertain events by buying or selling securities contingent on their outcomes. Each agent acts in the market so as to maximize expected utility at given securities prices, limited in its activity only by its own risk aversion. The equilibrium prices of goods in this market represent aggregate beliefs. For agents with constant risk aversion, we demonstrate that the aggregate probability exhibits several desirable properties, and is related to independently motivated techniques. We argue that the market-based approach provides a plausible mechanism for belief aggregation in multiagent systems, as it directly addresses self-motivated agent incentives for participation and for truthfulness, and can provide a decision-theoretic foundation for the "expert weights" often employed in centralized pooling techniques. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #683294. 	[Title] Toward a Market Model for Bayesian Inference [Abstract] We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and producers trade in uncertain propositions. We demonstrate the correspondence between the equilibrium prices of goods in this economy and the probabilities represented by the Bayesian network. A computational market model such as this may provide a useful framework for investigations of belief aggregation, distributed probabilistic inference, resource allocation under uncertainty, and other problems of de centralized uncertainty. Please summarise all the given information.

Paper #1132857 has the title `A Market Framework for Pooling Opinions  
` and the abstract `Consider a group of Bayesians, each with a subjective probability distribution over a set of uncertain events. An opinion pool derives a single consensus distribution over the events, representative of the group as a whole. Several pooling functions have been proposed, each sensible under particular assumptions or measures. Many researchers over many years have failed to form a consensus on which method is best. We propose a market-based pooling procedure, and analyze its properties. Participants bet on securities, each paying off contingent on an uncertain event, so as to maximize their own expected utilities. The consensus probability of each event is defined as the corresponding security's equilibrium price. The market framework provides explicit monetary incentives for participation and honesty, and allows agents to maintain individual rationality and limited privacy. "No arbitrage" arguments ensure that the equilibrium prices form legal probabilities. We show that, when events are disjoint and all participants have exponential utility for money, the market derives the same result as the logarithmic opinion pool; similarly, logarithmic utility for money yields the linear opinion pool. In both cases, we prove that the group's behavior is, to an outside observer, indistinguishable from that of a rational individual, whose beliefs equal the equilibrium prices. 
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Question: Which category should Paper #1132857 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1132857 has the title `A Market Framework for Pooling Opinions  
` and the abstract `Consider a group of Bayesians, each with a subjective probability distribution over a set of uncertain events. An opinion pool derives a single consensus distribution over the events, representative of the group as a whole. Several pooling functions have been proposed, each sensible under particular assumptions or measures. Many researchers over many years have failed to form a consensus on which method is best. We propose a market-based pooling procedure, and analyze its properties. Participants bet on securities, each paying off contingent on an uncertain event, so as to maximize their own expected utilities. The consensus probability of each event is defined as the corresponding security's equilibrium price. The market framework provides explicit monetary incentives for participation and honesty, and allows agents to maintain individual rationality and limited privacy. "No arbitrage" arguments ensure that the equilibrium prices form legal probabilities. We show that, when events are disjoint and all participants have exponential utility for money, the market derives the same result as the logarithmic opinion pool; similarly, logarithmic utility for money yields the linear opinion pool. In both cases, we prove that the group's behavior is, to an outside observer, indistinguishable from that of a rational individual, whose beliefs equal the equilibrium prices. 
`.
Question: Which category should Paper #1132857 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods