We consider two ways to aggregate expert opinions using simple averages: averaging probabilities and averaging quantiles. We examine analytical properties of these forecasts and compare their ability to harness the wisdom of the crowd. In terms of location, the two average forecasts have the...

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...

Probability forecasts of binary events are often gathered from multiple models and averaged to provide inputs regarding uncertainty in important decision-making problems. Averages of well calibrated probabilities are underconfident, and methods have been proposed to make them more extreme. To...

We explore some recent, and not so recent, developments concerning the use of probability forecasts and their combination in decision making. Despite these advances, challenges still exist. We expand on some important challenges influencing the “goodness” of combined probability forecasts...