The structure of neutral monotonic social functions (Q1111904)

We show that neutral monotonic social functions and their specializations to social functions, quasi-transitive social decision functions, and social welfare functions can be uniquely represented as a collection of overlapping simple games, each of which is defined on a nonempty set of concerned individuals. Moreover, each simple game satisfies certain intersection conditions depending on the number of social alternatives; the number of individuals belonging to the concerned set under consideration; and the collective rationality assumption.