A Note on Sandroni-Shmaya Belief Elicitation Mechanism

Abstract

Incentive-compatible methods for eliciting beliefs, such as proper scoring rules, often rely on strong assumptions about how humans behave when making decisions under risk and uncertainty. For example, standard proper scoring rules assume that humans are risk neutral, an assumption that is often violated in practice. Under such an assumption, proper scoring rules induce honest reporting of beliefs, in a sense that experts maximize their expected scores from a proper scoring rule by honestly reporting their beliefs.Sandroni and Shmaya [Economic Theory Bulletin, volume 1, issue 1, 2013] suggested a remarkable mechanism based on proper scoring rules that induces honest reporting of beliefs without any assumptions on experts’ risk attitudes. In particular, the authors claimed that the mechanism relies only on the natural assumptions of probabilistic sophistication and dominance. We suggest in this paper that the reduction of compound lotteries axiom is another assumption required for Sandroni and Shmaya’s mechanism to induce honest reporting of beliefs. We further elaborate on the implications of such an extra assumption in light of recent findings regarding the reduction of compound lotteries axiom.