Measures of the Value of Information

McCarthy, John

doi:10.1073/pnas.42.9.654

Cited by 158 publications

(91 citation statements)

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“…The forecaster's optimal expected score that is obtained when her distribution is p will be denoted by merely suppressing the first argument: S p ≡ S p p . A proper scoring rule is uniquely determined by its optimal-expected-score function, as noted by McCarthy (1956) and further elaborated by Hendrickson and Buehler (1971) and Savage (1971). In particular, if S · is a differentiable function, then S · · satisfies…”

Section: Weighted Scoring Rulesmentioning

confidence: 99%

Scoring Rules, Generalized Entropy, and Utility Maximization

Jose

Nau

Winkler

2008

Operations Research

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Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision analysis (where new information can lead to improved decisions), and finance (where investors optimize portfolios based on their private information and risk preferences). In this paper, we generalize the two most commonly used parametric families of scoring rules and demonstrate their relation to well-known generalized entropies and utility functions, shedding new light on the characteristics of alternative scoring rules as well as duality relationships between utility maximization and entropy minimization. In particular, we show that weighted forms of the pseudospherical and power scoring rules correspond exactly to measures of relative entropy (divergence) with convenient properties, and they also correspond exactly to the solutions of expected utility maximization problems in which a risk-averse decision maker whose utility function belongs to the linear-risk-tolerance family interacts with a risk-neutral betting opponent or a complete market for contingent claims in either a one-period or a two-period setting. When the market is incomplete, the corresponding problems of maximizing linear-risk-tolerance utility with the risk-tolerance coefficient are the duals of the problems of minimizing the pseudospherical or power divergence of order between the decision maker's subjective probability distribution and the set of risk-neutral distributions that support asset prices.

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Section: Weighted Scoring Rulesmentioning

confidence: 99%

Scoring Rules, Generalized Entropy, and Utility Maximization

Jose

Nau

Winkler

2008

Operations Research

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“…It turns out that the logarithmic scoring rule is the unique proper scoring rule that has this property amongst differentiable scoring rules. McCarthy (1956) …”

Section: Selecting Between Proper Scoring Rulesmentioning

confidence: 99%

A penny for your thoughts: a survey of methods for eliciting beliefs

2014

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Incentivized methods for eliciting subjective probabilities in economic experiments present the subject with risky choices or bets that encourage truthful reporting. We discuss the most prominent elicitation methods and their underlying assumptions, provide theoretical comparisons, and propose some extensions to the standard framework. In addition, we survey the empirical literature on the performance of these elicitation methods in actual experiments, considering also practical issues of implementation such as order effects, hedging, and different ways of presenting probabilities and payment schemes to experimental subjects. We end with some thoughts on the merits of using incentives for belief elicitation and some guidelines for implementation. JEL-codes: C83, C91, D83.

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“…The expected value of such a function in any strictly proper decision market is a∈A o∈O Q a,o 1 |A| G(P ) − G (P ) : P + |A|G a,o (P ) = G(P ) − G (P ) : P + a∈A o∈O Q a,o G a,o (P ), the same as the expected value of a prediction in a set of m prediction markets with outcomes O using a multi-scoring rule of the form given in (14). This is the correspondence Theorem 4 exploits.…”

Section: B Our Bayesian Model and Proof Of Theoremmentioning

confidence: 99%

Decision Markets with Good Incentives

Kash

Ruberry

Shnayder

2011

Lecture Notes in Computer Science

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Abstract. Decision and prediction markets are designed to determine the likelihood of future events; prediction markets predict what will happen, and decision markets predict the results of a choice, or what would happen. Both allow multiple participants to review and make predictions, and participants are typically scored for improving the accuracy of the market's prediction. Previous work has demonstrated prediction markets can reward accuracy improvements, as can a single participant informing a decision. We construct and characterize decision markets where all participants are scored for improving the market's accuracy. These markets require the decision maker always risk taking an action at random, and reducing this risk increases its potential loss. We also relate these decision markets to sets of prediction markets, demonstrating a correspondence between their perfect Bayesian equilibria.

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Measures of the Value of Information

Cited by 158 publications

References 0 publications

Scoring Rules, Generalized Entropy, and Utility Maximization

Scoring Rules, Generalized Entropy, and Utility Maximization

A penny for your thoughts: a survey of methods for eliciting beliefs

Decision Markets with Good Incentives

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