Eliciting Truthful Answers to Multiple-Choice Questions Preliminary Report

Motivated by the prevalence of online questionnaires in electronic commerce, and of multiple-choice questions in such questionnaires, we consider the problem of eliciting truthful answers to multiple-choice questions from a knowledgeable respondent. Specifically, each question is a statement regarding an uncertain future event, and is multiple-choice - the responder must select exactly one of the given answers. The principal offers a payment, whose amount is a function of the answer selected and the true outcome (which the principal will eventually observe). Tins problem significantly generalizes recent work on truthful elicitation of distribution properties, which itself generalized a long line of work in elicitation of complete distributions. We provide necessary and sufficient; conditions for the existence of payments that induce truthful answers, and give a characterization of those payments. We also study in greater details the common case of questions with ordinal answers, and illustrate our results with several examples of practical interest.