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.