I've previously mentioned the shortest splitline algorithm for determining congressional districts in the United States. (This could work in other districting situations, as well.) The algorithm breaks states into districts by breaking them up along the shortest possible lines; for a more thorough description see this.
Well, today I got an e-mail from the good people at rangevoting.org saying that they now had computer-generated maps of their algorithm's redistrictings for all fifty states. These, I assume, supercede their approximate sketches
I'm not entirely sure how good an idea this particular redistricting algorithm is. Basically, assuming that straight lines are the right way to break things up seems to imply that all directions should be treated equally, when actual settlement patterns aren't isotropic. But the beauty of any algorithm which doesn't include any "tunable" parameters -- of which this is an example -- is that there is zero possibility of gerrymandering. If we imagine an algorithm that takes into account "travel time" between points, for example, instead of as-the-crow-flies distance, then how do you define travel time? And next thing you know, you'll see new roads getting built because of how you'd expect them to change congressional districting. As-the-crow-flies distance along the surface of the earth doesn't have these issues.
Not surprisingly, the people at rangevoting.org also support something called range voting, which would basically allow people to give scores to candidates in an election, and the candidate with the highest scores would win. I haven't much thought about it, but it seems like a good idea. And here's their page for mathematicians!