[zerebubuth]

I think you're absolutely correct!

In each round, I reckon the optimal strategy for the "cut" will likely be the same as partisan cuts are now; densely pack the opposition's supporters into a small number of districts, while slicing the rest up to have a small but stable majority for one's own party.

This gives the opposition the chance to choose/freeze either a district they know they'll win, or a district they're pretty sure they won't win. I would choose the one I know my party would win, and redraw to pack all my opposition's voters into as few districts as possible.

If this is repeated a few times, the map ends up with many safe districts for each party and a small number of "left-overs" which will be contested. This means parties will have an incentive to concentrate on the small number of voters in the few contestable districts, at the expense of probably the majority of voters. It doesn't seem like a recipe for every vote counting and voters' voices being listened to.

If we break up monopoly businesses when the lack of choice increases the cost to consumers, should we also break up monopoly parties when the lack of choice increases the "cost" in time and effort that voters must "spend" to get their issues dealt with?