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
Reduction in Belief Elicitation