An Axiomatic View of the Parimutuel Consensus Mechanism

We consider an axiomatic view of the Parimutuel Consensus Mechanism defined by Eisenberg and Gale (1959). The parimutuel consensus mechanism can be interpreted as a parimutuel market for wagering with a proxy that bets optimally on behalf of the agents, depending on the bets of the other agents.  We show that the parimutuel consensus mechanism uniquely satisfies the desirable properties of Pareto optimality, individual rationality, budget balance, anonymity, sybilproofness and envy-freeness. While the parimutuel consensus mechanism does violate the key property of incentive compatibility, it is incentive compatible in the limit as the number of agents becomes large. Via simulations on real contest data, we show that violations of incentive compatibility are both rare and only minimally beneficial for the participants. This suggests that the parimutuel consensus mechanism is a reasonable mechanism for eliciting information in practice.