Researchers commonly elicit a precise belief about the probability of an event. But often, precision is not required, and it is sufficient to determine which of some set of probabilities is closest to a participant's belief. We show that, among the many suitable scoring rules for eliciting a precise belief, only quadratic rules are suitable for eliciting coarsely. However, scoring rules are not the only way to elicit a belief. We propose two types of simple menu procedures as an alternative to using a quadratic scoring rule to elicit coarsely. These procedures are simple, flexible, and incentive compatible under assumptions nearly universal to experimental economics.
Healy, P.J. and Leo, Greg, Coarse Belief Eclicitation