Further evidence against independence preservation in expert judgement synthesis

Genest, Christian; Wagner, Carl

doi:10.1007/bf02311302

Cited by 32 publications

(38 citation statements)

References 15 publications

(8 reference statements)

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“…For example, it is possible in this language to have a market distribution in which the winners of first round games are not independent of one another. This phenomenon relates to results on the impossibility of preserving independence in an aggregate distribution [6,13]. We show that the usual independence relationships are restored if we only permit bets of the form "team i beats team j given that they face off".…”

Section: Introductionmentioning

confidence: 68%

Pricing combinatorial markets for tournaments

Chen

Goel

Pennock

2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

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In a prediction market, agents trade assets whose value is tied to a future event, for example the outcome of the next presidential election. Asset prices determine a probability distribution over the set of possible outcomes. Typically, the outcome space is small, allowing agents to directly trade in each outcome, and allowing a market maker to explicitly update asset prices. Combinatorial markets, in contrast, work to estimate a full joint distribution of dependent observations, in which case the outcome space grows exponentially. In this paper, we consider the problem of pricing combinatorial markets for single-elimination tournaments. With n competing teams, the outcome space is of size 2 n−1 . We show that the general pricing problem for tournaments is #P-hard. We derive a polynomial-time algorithm for a restricted betting language based on a Bayesian network representation of the probability distribution. The language is fairly natural in the context of tournaments, allowing for example bets of the form "team i wins game k". We believe that our betting language is the first for combinatorial market makers that is both useful and tractable. We briefly discuss a heuristic approximation technique for the general case.

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Section: Introductionmentioning

confidence: 68%

Pricing combinatorial markets for tournaments

Chen

Goel

Pennock

2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

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“…In general, non-dictatorial pooling methods struggle with independence preservation (Genest and Wagner, 1987). (Here, too, we claim to do better.…”

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confidence: 90%

“…The normative status of this sort of preservation axiom has been called into question in the literature (Genest and Wagner, 1987). Of course, ZPP is forced upon those endorsing SSFP.…”

Section: Poolingmentioning

confidence: 99%

Probabilistic Opinion Pooling with Imprecise Probabilities

Stewart

Quintana

2017

J Philos Logic

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Abstract. The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution (Madansky, 1964;Lehrer and Wagner, 1981;McConway, 1981;Bordley, 1982;Genest and Zidek, 1986;Mongin, 1995;Clemen and Winkler, 1999;Dietrich and List, 2014;Herzberg, 2014). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities (IP) by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi (1985), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus.

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“…In fairness, we should mention that the failure to preserve probabilistic independence can be held not just against eventwise independent pooling functions but against a much wider class of pooling functions (Genest and Wagner 1987). This includes all linear, geometric, and multiplicative pooling functions that are non-dictatorial.…”

Section: The Limitations Of Eventwise Independent Aggregationmentioning

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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Further evidence against independence preservation in expert judgement synthesis

Cited by 32 publications

References 15 publications

Pricing combinatorial markets for tournaments

Pricing combinatorial markets for tournaments

Probabilistic Opinion Pooling with Imprecise Probabilities

Probabilistic Opinion Pooling

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