Efficient interval scoring rules

Scoring rules that elicit an entire belief distribution through the elicitation of point beliefs are time-consuming and demand considerable cognitive e¤ort. Moreover, the results are valid only when agents are risk-neutral or when one uses probabilistic rules. We investigate a class of rules in which the agent has to choose an interval and is rewarded (deterministically) on the basis of the chosen interval and the realization of the random variable. We formulate an e¢ ciency criterion for such rules and present a speci.c interval scoring rule. For single- peaked beliefs, our rule gives information about both the location and the dispersion of the belief distribution. These results hold for all concave utility functions.