Abstract

We develop the first incentive compatible and near-Pareto-optimal wagering mechanism. Wagering mechanisms can be used to elicit predictions from agents who reveal their beliefs by placing bets. Lambert et al. [20, 21] introduced weighted score wagering mechanisms, a class of budget-balanced wagering mechanisms under which agents with immutable beliefs truthfully report their predictions. However, we demonstrate that these and other existing incentive compatible wagering mechanisms are not Pareto optimal: agents have significant budget left over even when additional trade would be mutually beneficial. Motivated by this observation, we design a new wagering mechanism, the double clinching auction, a two-sided version of the adaptive clinching
auction [9]. We show that no wagering mechanism can simultaneously satisfy weak budget balance, individual rationality, weak incentive compatibility, and Pareto optimality. However, we prove that the double clinching auction attains the first three and show in a series of simulations using real contest data that it comes much closer to Pareto optimality than previously known incentive compatible wagering mechanisms, in some cases almost matching the efficiency of the Pareto optimal (but not incentive compatible) parimutuel consensus mechanism. When the goal of wagering is to crowdsource probabilities, Pareto optimality drives participation and incentive compatibility drives accuracy, making the double clinching auction an attractive and practical choice. Our mechanism may be of independent interest as the first two-sided version of the adaptive clinching auction.