Probability and Asset Updating using Bayesian Networks for Combinatorial Prediction Markets

Wei Sun, Robin Hanson, Kathryn Blackmond Laskey, Charles Twardy
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:814-823, 2012.

Abstract

A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a base set of events. However, explicitly representing the full joint distribution is infeasible for markets with more than a few base events. A factored representation such as a Bayesian network (BN) can achieve tractable computation for problems with many related variables. Standard BN inference algorithms, such as the junction tree algorithm, can be used to update a representation of the entire joint distribution given a change to any local conditional probability. However, in order to let traders reuse assets from prior trades while never allowing assets to become negative, a BN based prediction market also needs to update a representation of each user’s assets and find the conditional state in which a user has minimum assets. Users also find it useful to see their expected assets given an edit outcome. We show how to generalize the junction tree algorithm to perform all these computations.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-sun12a, title = {Probability and Asset Updating using {B}ayesian Networks for Combinatorial Prediction Markets}, author = {Sun, Wei and Hanson, Robin and Laskey, Kathryn Blackmond and Twardy, Charles}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {814--823}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/sun12a/sun12a.pdf}, url = {https://proceedings.mlr.press/r10/sun12a.html}, abstract = {A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a base set of events. However, explicitly representing the full joint distribution is infeasible for markets with more than a few base events. A factored representation such as a Bayesian network (BN) can achieve tractable computation for problems with many related variables. Standard BN inference algorithms, such as the junction tree algorithm, can be used to update a representation of the entire joint distribution given a change to any local conditional probability. However, in order to let traders reuse assets from prior trades while never allowing assets to become negative, a BN based prediction market also needs to update a representation of each user’s assets and find the conditional state in which a user has minimum assets. Users also find it useful to see their expected assets given an edit outcome. We show how to generalize the junction tree algorithm to perform all these computations.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Probability and Asset Updating using Bayesian Networks for Combinatorial Prediction Markets %A Wei Sun %A Robin Hanson %A Kathryn Blackmond Laskey %A Charles Twardy %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-sun12a %I PMLR %P 814--823 %U https://proceedings.mlr.press/r10/sun12a.html %V R10 %X A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a base set of events. However, explicitly representing the full joint distribution is infeasible for markets with more than a few base events. A factored representation such as a Bayesian network (BN) can achieve tractable computation for problems with many related variables. Standard BN inference algorithms, such as the junction tree algorithm, can be used to update a representation of the entire joint distribution given a change to any local conditional probability. However, in order to let traders reuse assets from prior trades while never allowing assets to become negative, a BN based prediction market also needs to update a representation of each user’s assets and find the conditional state in which a user has minimum assets. Users also find it useful to see their expected assets given an edit outcome. We show how to generalize the junction tree algorithm to perform all these computations. %Z Reissued by PMLR on 04 October 2026.
APA
Sun, W., Hanson, R., Laskey, K.B. & Twardy, C.. (2012). Probability and Asset Updating using Bayesian Networks for Combinatorial Prediction Markets. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:814-823 Available from https://proceedings.mlr.press/r10/sun12a.html. Reissued by PMLR on 04 October 2026.

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