New algorithm that can fairly divide a cake among any number of people

But what if the density of the cake matters?

Solve that one, and you can create a neutral algorithm to create voting districts across states and countries. That means you can put an end to gerrymandering forever; that will eliminate a lot extremist politics in Congress (etc) and the opinions of people whose views are more in the middle (and more representative) will start to count, again.

If density doesn't make sense to you, think of a U.S-shaped cake with a couple hundred million raisins, mostly clustered at the coasts. Now come up with an algorithm to divide that cake evenly into voting districts that are as circular as possible and each contain the same number of raisins, plus or minus one.

The counterargument is that cities gather left-leaning voters, so it wouldn't change as much as I'd like to think - but it would still help.