Belief Elicitation Using Binary-Choice Lists

Measuring people’s beliefs under uncertainty from incentivized choices can be reliable only under realistic assumptions about their preferences. How can we elicit various kinds of information about people’s beliefs under minimal assumptions? This paper develops a new theoretical framework to address this question. First, I characterize a key class of methods—binary-choice lists—which infer information about an individual’s subjective probability distribution from a set of pairwise choices among bets. Importantly, several known binary-choice lists elicit useful information under relatively weak assumptions. Second, using the characterization, I find that no method can elicit the same information under weaker assumptions, providing a new theoretical foundation for these lists. Third, I show that binary-choice lists are generally optimal relative to scoring rules, the other main class of elicitation methods, as under broad conditions, they require equivalent or weaker assumptions for eliciting the same information. These results guide the use and design of belief elicitation methods.