Purification of incentive compatible allocations (Q1416757)

The author considers a society composed of a finite number of types of individuals and a social choice function mapping those types into a probability distribution over an outcome space. This setting allows for a wide class of social choice functions, but there is something unsatisfactory about allowing for randomization of outcomes. The author seeks conditions under which a given social choice function may be replaced by a sufficiently close approximation where, for almost all types, the image is actually a point in the outcome space. Such approximations are called purifications. The author lists the desirable properties of the approximation and gives necessary conditions for the existence of a purification in the case that the outcome space is finite or countably infinite. The author also gives an existence proof for the continuous case under slightly differnet conditions.