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...

This note gives an easily verified necessary and sufficient condition for one probability forecaster to empirically outperform another one in terms of all strictly proper scoring rules.

The measurement of the quality of research has reached nowadays an increasing interest not only for scientific reasons but also for the critical problem of researchers' ranking, due to the lack of grant assignments. The most commonly used approach is based on the so-called $h$-index, even if the...

This paper studies a class of judgment aggregation rules, to be called `scoring rules' after their famous counterpart in preference aggregation theory. A scoring rule delivers the collective judgments which reach the highest total `score' across the individuals, subject to the judgments having...

In this paper I examine the Okun–Friedman hypothesis of the link between inflation and inflation uncertainty using historical international data on the monthly CPI. An indicator of inflation uncertainty at the two-years-ahead horizon is derived from a time-series model of inflation with...

Density forecast combinations are becoming increasingly popular as a means of improving forecast ‘accuracy’, as measured by a scoring rule. In this paper we generalise this literature by letting the combination weights follow more general schemes. Sieve estimation is used to optimise the...

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)...