How agents assess the (in-)tangible externalities that others might impose on them can strongly influence strategic interaction. This study explores mechanism design for agents whose externality assessments and private payoffs, exclusive of externalities, are all subject to asymmetric information. Under reasonable assumptions, the following result is established: Let the allocation rule f be the maximizer of a social welfare measure W that satisfies the Pareto property; then f is Bayesian implementable with an ex post budget-balanced mechanism if and only if W sums private payoffs exclusive of externalities. The result emphasizes the critical role of the value judgment inherent to the allocation rule. Bayesian implementation of a value judgment inconsistent with externality-ignoring utilitarianism violates budget balance and, thus, involves incentive costs. Cooperative models of bargaining are discussed in this light.