Restricted domains, arrow social welfare functions and noncorruptible and nonmanipulable social choice correspondences: The case of private and public alternatives

An n-person social choice problem is considered in which the alternatives are ( n + 1)-dimensional vectors, with the first component of such a vector being that part of the alternative affecting all the individuals together, while the ( i + 1) component is the part of the alternative affecting individual i alone. Assuming that individuals are selfish, that they may be indifferent among alternatives and that each individual may choose his preferences out of a different set of permissible preferences, we prove that any set of restricted domains of preferences admits an n-person nondictatorial, nonmanipulable and noncorruptible social choice correspondence.