2Bayesian paradigm. Following it, probability assessments and utility functions are defined independently. It seems reasonable to suggest that groups adopt a similar approach.3 That is, the group should deal separately with the two areas of potential disagreement. By some prescribed procedure, the group aggregates the individual probability assessments into a group probability assessment. Similarly, a group utility function is constructed by aggregating individual utility functions. The group probability assessment and utility function are multiplied in the usual manner to give expected utilities. The action offering the highest expected utility is chosen.4 Most real world decision processes, we recognize, make less than conscientious attempts to separate beliefs from values, either in debate or at time of decision.5

In a variety of contexts, individuals must be allocated to positions with limited capacities. Legislators must be assigned to committees, college students to dormitories, and urban homesteaders to dwellings. (A general class of fair division problems would have the positions represent goods.) This paper examines the general problem of achieving efficient allocations when individuals' preferences are unknown and where (as with a growing number of nonmarket allocation schemes) there is no facilitating external medium of exchange such as money. An implicit market procedure is developed that elicits honest preferences, that assigns individuals efficiently, and that is adaptable to a variety of distributional objectives.