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Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation
 Journal of Prediction Markets
, 2002
"... 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. ..."
Abstract

Cited by 74 (5 self)
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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.
Forecasting Binary Outcomes
, 2013
"... Binary events are involved in many economic decision problems. In recent years, considerable progress has been made in diverse disciplines in developing models for forecasting binary outcomes. We distinguish between two types of forecasts for binary events that are generally obtained as the output o ..."
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Cited by 2 (1 self)
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Binary events are involved in many economic decision problems. In recent years, considerable progress has been made in diverse disciplines in developing models for forecasting binary outcomes. We distinguish between two types of forecasts for binary events that are generally obtained as the output of regression models: probability forecasts and point forecasts. We summarize specification, estimation, and evaluation of binary response models for the purpose of forecasting in a unified framework which is characterized by the joint distribution of forecasts and actuals, and a general loss function. Analysis of both the skill and the value of probability and point forecasts can be carried out within this framework. Parametric, semiparametric, nonparametric, and Bayesian approaches are covered. The emphasis is on the basic intuitions underlying each methodology, abstracting away from the mathematical details.
Eliciting Objective Probabilities via Lottery Insurance Games
 Computational Mathematics Laboratory, Rice University
, 1993
"... Since utilities and probabilities jointly determine choices, eventdependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., proba ..."
Abstract

Cited by 1 (1 self)
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Since utilities and probabilities jointly determine choices, eventdependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent's further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had eventindependent riskneutral utility and a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities.
[Extended Abstract]
"... We investigate the problem of truthfully eliciting an expert’s assessment of a property of a probability distribution, where a property is any realvalued function of the distribution such as mean or variance. We show that not all properties are elicitable; for example, the mean is elicitable and th ..."
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We investigate the problem of truthfully eliciting an expert’s assessment of a property of a probability distribution, where a property is any realvalued function of the distribution such as mean or variance. We show that not all properties are elicitable; for example, the mean is elicitable and the variance is not. For those that are elicitable, we provide a representation theorem characterizing all payment (or “score”) functions that induce truthful revelation. We also consider the elicitation of sets of properties. We then observe that properties can always be inferred from sets of elicitable properties. This naturally suggests the concept of elicitation complexity; the elicitation complexity of property is the minimal size of such a set implying the property. Finally we discuss applications to prediction markets.