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Perhaps nice compact districts like this.
Anyway, we lack angels in the form of neutral experts to redistrict us.
My 55% serious solution is to redistrict via random parameters every six years, without any human input.
The key thing that makes the difference in the UK (and, AFIAK, other Commonwealth countries) is that there is a small amount of wiggle-room on equal electorates, allowing most districts to align with local government boundaries that change a lot less often than the redistricting cycle.
If the non-partisan merit criterion is "draw as many district boundaries on municipal boundaries as possible, conditional on all districts having equal electorates to within 5%" then there may even be a knowable optimum answer, and in any case there is less wiggle-room than "draw compact districts with exactly equal census populations" because you can't tweak boundaries at census tract level.
When the UK Boundary Commission consults on map changes, they get two types of response:
At least in the UK, real normie voters would rather be mildly under-represented than have an unnatural constituency drawn based on a size criterion. The textbook example is the Isle of Wight where the locals insisted on having a single constituency with 113k voters (vs a national target of 73k) rather than having 40k of them share an MP with part of the mainland. In my own mis-spent youth as a local politician when I was in grad school in Cambridge, Cambridge residents similarly felt that the City of Cambridge (c. 90k voters) should be a single constituency with an aligned boundary, although the Boundary Commission ignored them and drew right-size constituencies that put one ward into the adjacent rural seat. Uncontroversially, the whole county of Cambridgeshire got exactly 8 constituencies (with no constituency crossing the county line) despite an electorate that would justify about 8.2.
There can be a knowable optimum answer under those conditions, but in much of the US such a map would "pack" Democrats, giving Republicans a significant advantage -- that's why I posted the Florida map, which does pretty much that.
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My trolling solution is to randomly assign voters to districts: "look ma, no consideration at all of race, creed, or anything". Except that it's definitionally the worst possible gerrymander.
Honestly, I think geographic districting is a lost cause and proportional statewide representation would at least give easy answers to these problems.
I'm pretty sure this one of the Supreme Court partisan gerrymandering cases had this exact fact-pattern. They wrote a computer program to generate hundreds of possible maps that all comply with "traditional districting criteria", then picked the map that had the most Republican seats.
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