The Binarized Scoring Rule

Abstract

We introduce a simple method for constructing a scoring rule to elicit an agent's belief about a random variable that is incentive compatible irrespective of her risk-preference. The agent receives a fixed prize when her prediction error, defined by a loss function specified in the incentive scheme, is smaller than an independently generated random number and earns a smaller prize otherwise. Adjusting the loss function according to the belief elicitation objective, the scoring rule can be used in a rich assortment of situations. Moreover, the scoring rule can be incentive compatible even when the agent is not an expected utility maximizer. Results from our probability elicitation experiments show that subjects' predictions are closer to the true probability under this scoring rule compared to the quadratic scoring rule.