The structure of continuous-valued neutral monotonic social functions (Q1066784)

Let A be a compact convex set of social states in \(R^ m\) and I a finite set of voters. Each voter i has a continuous convex preference relation \(P_ i\) defined on A. \(W^ I\) denotes the product space of individual preference relations. A social function is a mapping from \(W^ I\) into the set of all preference relations on A. A social decision function is a mapping from \(W^ I\) into the set of all preference relations on A such that the set of undominated alternatives is nonempty. The paper contains two major results on neutral monotonic functions. A social function is continuous-valued if and only if it is completely determined by a single set of decisive coalitions. Moreover, a social decision function (continuous-valued) need not have a veto player if the number of voters exceeds \(m+1\). These results generalize well-known results due to Blau and Brown, and Greenberg.