I've got an educational game in the work that challenges players to redraw U.S. state borders in a way that reduce the inequality between big-population and small-population states. As they play, they need to get real-time feedback on the effect of assigning counties from one state to another.
So I need some sort of single parameter of "equalness" that is derived from the distribution of populations in the new hypothetical set of states.
I've thought about just displayed the standard deviation in the state populations. Is there a better way to succinctly express a power distribution? I'd prefer something as simple to understand as possible since I want to appeal to a broad audience. State populations as of 2010 Census below for reference.