Partitioning the Vote

My earlier notion for preventing gerrymandering was not very effective. Looking at the data for the Michigan 2018 election, the Democrats had a majority of the vote but a minority of the districts. My proposed rule would have done nothing to prevent that.

Exactly what a good rule might be, I don't know. It's a difficult problem! But the basic criterion that seems logical is that the fraction of districts won by each party should be roughly proportional to the fraction of votes for that party. A general shift in voter preference should be reflected with a proportional shift in election results, in the fraction of districts won by a party. This would be achieved by having district boundaries drawn so that the fractions of votes for each party across the districts varies across a reasonably wide spectrum.

The challenge with this approach is that the notion of "a general shift" is too vague to be of much use. Still, a simple model can get the idea across.

Here is an idealized situation, a state with ten districts. When the vote is split equally, the range of district results could be:

With a general drift to 60% of the vote for one of the parties, the number of districts won could change proportionally:

A further shift, to 70%, would continue to be reflected in the proportion of districts won: