An Equivalence between Wagering and Fair-Division Mechanisms

Abstract

We draw a surprising and direct mathematical equivalence between the class of allocation mechanisms for divisible goods studied in the context of fair division and the class of weakly budget-balanced wagering mechanisms designed for eliciting probabilities. The equivalence rests on the intuition that wagering is an allocation of financial securities among bettors, with a bettor’s value for each security proportional to her belief about the likelihood of a future event. The equivalence leads to theoretical advances and new practical approaches for both fair division and wagering. Known wagering mechanisms based on proper scoring rules yield fair allocation mechanisms with desirable properties, including the first strictly incentive compatible fair-division mechanism. At the same time, allocation mechanisms make for novel wagering rules, including one that requires only ordinal uncertainty judgments and one that outperforms existing rules in a range of simulations.