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Information markets vs. opinion pools: An empirical comparison
 In Proceedings of the Sixth ACM Conference on Electronic Commerce (EC’05
, 2005
"... In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people’s subjective probability judgments on 2003 US National Football League games and compare with the “market probabilities ” given by two dif ..."
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Cited by 22 (9 self)
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In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people’s subjective probability judgments on 2003 US National Football League games and compare with the “market probabilities ” given by two different information markets on exactly the same events. We combine assessments of multiple experts via linear and logarithmic aggregation functions to form pooled predictions. Prices in information markets are used to derive market predictions. Our results show that, at the same time point ahead of the game, information markets provide as accurate predictions as pooled expert assessments. In screening pooled expert predictions, we find that arithmetic average is a robust and efficient pooling function; weighting expert assessments according to their past performance does not improve accuracy of pooled predictions; and logarithmic aggregation functions offer bolder predictions than linear aggregation functions. The results provide insights into the predictive performance of information markets, and the relative merits of selecting among various opinion pooling methods.
VINCENTIZATION REVISITED BY CHRISTIAN GENEST
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Advances: Aggregate Probabilities Page 1 of 39 Ch 09 060430 V07 9 Aggregation of Expert Probability Judgments
"... probability distributions from experts in risk analysis, ” Risk Analysis, 19, 187203. This chapter is concerned with the aggregation of probability distributions in decision and risk analysis. Experts often provide valuable information regarding important uncertainties in decision and risk analyses ..."
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probability distributions from experts in risk analysis, ” Risk Analysis, 19, 187203. This chapter is concerned with the aggregation of probability distributions in decision and risk analysis. Experts often provide valuable information regarding important uncertainties in decision and risk analyses because of the limited availability of “hard data ” to use in those analyses. Multiple experts are often consulted in order to obtain as much information as possible, leading to the problem of how to combine or aggregate their information. Information may also be obtained from other sources such as forecasting techniques or scientific models. Because uncertainties are typically represented in terms of probability distributions, we consider expert and other information in terms of probability distributions. We discuss a variety of models that lead to specific combination methods. The output of these methods is a “combined probability distribution, ” which can be viewed as representing a summary of the current state of information regarding the uncertainty of interest. After presenting the models and methods, we discuss empirical evidence on the performance of the methods. In the conclusion we highlight important
CARL G. WAGNER CONSENSUS FOR BELIEF FUNCTIONS AND RELATED UNCERTAINTY MEASURES*
"... ABSTRACT. We extend previous work of Lehrer and Wagner, and of McConway, on the consensus of probabilities, showing under axioms similar to theirs that (1) a belief function consensus of belief functions on a set with at least three members and (2) a belief function consensus of Bayesian belief func ..."
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ABSTRACT. We extend previous work of Lehrer and Wagner, and of McConway, on the consensus of probabilities, showing under axioms similar to theirs that (1) a belief function consensus of belief functions on a set with at least three members and (2) a belief function consensus of Bayesian belief functions on a set with at least four members must take the form of a weighted arithmetic mean. We observe that these results are unchanged when consensual uncertainty measures are allowed to take the form of Choquet capacities of low order monotonicity.
C. Defendant liable?
, 2005
"... In political science and legal theory, the doctrinal paradox (or discursive dilemma) is the observation that if a group of voters casts separate ballots on each proposition of a given agenda, and the majority rule is applied to each of these votes, the resulting set of propositions may be logicall ..."
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In political science and legal theory, the doctrinal paradox (or discursive dilemma) is the observation that if a group of voters casts separate ballots on each proposition of a given agenda, and the majority rule is applied to each of these votes, the resulting set of propositions may be logically inconsistent. Example discussed in List and Pettit (2002). A court decides whether a defendant is liable under a charge of breach of contract. The judges will find against the defendant iff they conclude that a valid contract was made and the defendant broke that existing valid contract. So the three questions to be answered are:
Graphical Representations of Consensus Belief
"... Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone ..."
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Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone agrees on a common graph topology, no method of combining beliefs can maintain that structure. Even weaker conditions rule out local aggregation within conditional probability tables. On a more positive note, we show that if probabilities are combined with the logarithmic opinion pool (LogOP), then commonly held Markov independencies are maintained. This suggests a straightforward procedure for constructing a consensus Markov network. We describe an algorithm for computing the LogOP with time complexity comparable to that of exact Bayesian inference. 1
ABSTRACT Information Markets vs. Opinion Pools: An Empirical Comparison
"... In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people’s subjective probability judgments on 2003 US National Football League games and compare with the “market probabilities ” given by two dif ..."
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In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people’s subjective probability judgments on 2003 US National Football League games and compare with the “market probabilities ” given by two different information markets on exactly the same events. We combine assessments of multiple experts via linear and logarithmic aggregation functions to form pooled predictions. Prices in information markets are used to derive market predictions. Our results show that, at the same time point ahead of the game, information markets provide as accurate predictions as pooled expert assessments. In screening pooled expert predictions, we find that arithmetic average is a robust and efficient pooling function; weighting expert assessments according to their past performance does not improve accuracy of pooled predictions; and logarithmic aggregation functions offer bolder predictions than linear aggregation functions. The results provide insights into the predictive performance of information markets, and the relative merits of selecting among various opinion pooling methods.
Christian List
, 2013
"... We introduce a “reasonbased ” way of rationalizing an agent’s choice behaviour, which explains choices in terms of “motivationally salient ” properties of the options and/or the choice context, thereby explicitly modelling the agent’s conceptualization of a given choice problem. Reasonbased ration ..."
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We introduce a “reasonbased ” way of rationalizing an agent’s choice behaviour, which explains choices in terms of “motivationally salient ” properties of the options and/or the choice context, thereby explicitly modelling the agent’s conceptualization of a given choice problem. Reasonbased rationalizations can explain nonclassical choice behaviour, including boundedly rational and sophisticated rational behaviour, and predict choices in unobserved contexts. We examine the behavioural implications of di↵erent reasonbased models and distinguish two kinds of contextdependent motivation: “contextvariant ” motivation, where di↵erent choice contexts make di↵erent properties motivationally salient, and “contextregarding” motivation, where the agent cares not only about properties of the options themselves, but also about properties relating to the choice context. 1
1 An Impossibility Theorem for Allocation Aggregation
"... Abstract Among the many sorts of problems encountered in decision theory, allocation problems occupy a central position. Such problems call for the assignment of a nonnegative real number to each member of a finite (more generally, countable) set of entities, in such a way that the values so assigne ..."
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Abstract Among the many sorts of problems encountered in decision theory, allocation problems occupy a central position. Such problems call for the assignment of a nonnegative real number to each member of a finite (more generally, countable) set of entities, in such a way that the values so assigned sum to some fixed positive real number.s Familiar cases include the problem of specifying a probability mass function on a countable set of possible states of the world ( 1),s and the distribution of a certain sum of money, or other resource, among various enterprises. In determining an sallocation it is common to solicit the opinions of more than one individual, which leads immediately to the question of how to aggregate their typically differing allocations into a single “consensual ” allocation. Guided by the traditions of social choice theory (in which the aggregation of preferential orderings, or of utilities is at issue) decision theorists have taken an axiomatic approach to determining acceptable methods of allocation aggregation. In such approaches socalled “independence ” conditions have been ubiquitous. Such conditions dictate that the consensual allocation assigned to each entity should depend only on the allocations assigned by individuals to that entity, taking no account of the allocations that they assign to any other entities. While there are reasons beyond mere simplicity for subjecting