For those who want to seriously crunch numbers (or who can point to a source who already has)
Is it possible to get every state to draw congressional districts assuring that the Partisan Voting Index is no more than 10 percentage points (one party or the other)?
I believe PVI is calculated relative to the vote shares in presidential elections. Therefore, it would be impossible to do so in any state with PVI > 10 in either direction. My knowledge of PVI is rather hazy, so if anyone wants to correct me, please do.
Also, I question why this would be a good aim. Making all districts competitive would itself be a sort of gerrymandering, since you'd have to throw out any notion of community of interest in order to make ultra-Democratic cities have competitive districts.
