Consider a society o...

We construct a budget-balanced wagering mechanism that flexibly extracts infor-mation about event probabilities, as well as the mean, median and other statistics from a group of individuals. We show how our mechanism, called Brier betting mechanism, arises naturally from a modified parimutuel betting market. We prove that it is es-sentially the unique wagering mechanism that is anonymous, proportional, sybilproof, and homogeneous. In a Bayesian setting, we find that a slight bias away from truthful reporting may arise under asymmetric information, through the correlation between the total wealth wagered and the event outcome. The bias is driven towards zero as the fraction of any individual’s wealth compared to the group converges towards zero