Cardinal Bayesian allocation mechanisms without transfers

In allocating goods with no use of monetary transfers, random allocation mechanisms can be designed in order to elicit information on preference intensities. I study the nontransfer allocation of two ex-ante identical objects under Bayesian incentive compatibility, with symmetric agents and independent private valuations. I …nd the ex-ante utilitarian-optimal mechanism, in which the probability of receiving a speci…ed object is used as "numeraire" to purchase probability units of the other object. I characterize this mechanism as an appropriate combination of lotteries, auctions and insurance. The latter element ensures that e¢ cient auctions are feasible. If the problem is constrained to guarantee exactly one object per agent, then the optimal mechanism uses no more information than the agents’ordinal preferences.