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...

An individual is repeatedly offered the opportunity to invest in a risky asset whose return distribution is unknown. Because the return distribution is constant over time, however, he is able to learn about that distribution by observing investment outcomes. Results are presented regarding the...