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...