Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation
| Abstract | In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of base event pairs, it costs no more to elicit estimates on all combinations of these base events. | |||||||||
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Joel Predd, Robert Seiringer, Elliott Lieb, Daniel Osherson, H. Vincent Poor & Sanjeev Kulkarni (2009). Probabilistic Coherence and Proper Scoring Rules. IEEE Transactions on Information Theory 55 (10):4786-4792.
R. Portugal & B. Svaiter (2011). Weber-Fechner Law and the Optimality of the Logarithmic Scale. Minds and Machines 21 (1):73-81.
Dominique Lepelley, Patrick Pierron & Fabrice Valognes (2000). Scoring Rules, Condorcet Efficiency and Social Homogeneity. Theory and Decision 49 (2):175-196.
Herman Dishkant (1980). Three Prepositional Calculi of Probability. Studia Logica 39 (1):49 - 61.
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