Consider a decision problem involving a group of m Bayesians in which each member reports his/her posterior distribution for some random variable \theta . The individuals all share a common prior distribution for \theta and a common loss function, but form their posterior distributions based on...

Scoring rules can provide incentives for truthful reporting of probabilities and evaluation measures for the probabilities after the events of interest are observed. Often the space of events is ordered and an evaluation relative to some baseline distribution is desired. Scoring rules typically...

We present a novel methodology for identifying public knowledge and eliminating the biases it creates when aggregating information in small group settings. A two-stage mechanism consisting of an information market and a coordination game is used to reveal and adjust for individuals' public...

Proper scoring rules are over evaluation measures that reward accurate probabilities Specific rules encountered in the literature and used in practice are invariably symmetric in the sense that the expected score for a perfectly-calibrated probability assessor (or model generating probabilities)...

Probability forecasters who are rewarded via a proper scoring rule may care not only about the score, but also about their performance relative to other forecasters. We model this type of preference and show that a competitive forecaster who wants to do better than another forecaster typically...