Two-tier voting: Measuring inequality and specifying the inverse power problem

•The coefficient of variation appropriately measures inequality in voting settings.•The coefficient of variation is appropriate to specify the inverse power problem.•This specification is equivalent to using a particular distance-based error term.

There are many situations in which different groups make collective decisions by committee voting, with each group represented by a single person. This paper is about two closely related problems. The first is that of how to measure the inequality of a voting system in such a setting. The second is the inverse power problem: the problem of finding voting systems that approximate equal indirect voting power as well as possible. I argue that the coefficient of variation is appropriate to measure the inequality of a voting system and to specify the inverse problem. I then show how specifying the inverse problem with the coefficient of variation compares to using existing objective functions.