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How would you define an administrative district? It's likely similar I'd imagine, but not sure where your frame of reference comes from.
Well I don't need to, they are predefined administrative units. Take the federal state of Northrhine-Westphalia in Germany as an example:
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In the US, after a census every 10 years, each state is allocated a number of House congressional districts based on population. The House has 435 members (not including non-voting members from territories like Puerto Rico). The number for any given state fluctuates each census, so predefined districts won't work.
One way to combat gerrymandering without a constitutional amendment is to increase the size of the House. It's set by statute and hasn't been changed since 1911.
Another is to use Iowa's redistricting method, which has appropriately boring maps: https://waynecountyelections.iowa.gov/global/maps/iowa_congressional_districts_82470.pdf
Ideally it makes sense to divide districts based on population. But the elections system in the US has so many flaws, it feels like optimizing at the wrong position.
I mean if you subsume the votes under the "state level" in a first step, wouldn't it be logical to go the next step subsume under county level (or whatever your administrative units are being called)?
Division based on population can never be stable because people are moving, so I feel this is the wrong metric in the first place.
Again I am not living in the US, so if I made some wrong assumptions please correct me. I don't know much about your election system.
The Iowa method is basically collecting the counties together into roughly equal population. But states get a lot of leeway in the exact methods.
(Aside: it's weird that the US uses that term in most states, because none of it was ever ruled by Counts. Although Louisiana does call them a "Parish" instead, which is a weirdly religious term for effectively the same thing.)
Increasing the size of the House would also increase the number of electoral college votes and would make it far less likely that there's a split between the electoral college and popular vote. So doing that and replacing first-past-the-post voting covers pretty much everything structurally wrong with the US election system.
Are all of these the same population size? That is roughly what our districts are, partitions of our populace into ~equal regions. Our nearest second level partition would be counties, which are drawn based on characteristics that largely remained static since their creation (1600s). Districts are generally redrawn every 10 years, but well… here we are.
In theory, districts are supposed to be race blind, and group together people based on rough location. But they don’t necessarily need to be the least complex shapes (hexagons), because that generally isn’t how humans have settled in areas. Again, in theory it was meant to capture groupings of people who would want or deserve similar representation but aren’t optimally clumped together. Instead, both sides have abused the lack of simple shapes rule to really fuck with representation. In particular, these last 20 years have seen the worst gerrymandering abuses because computing power progress made it feasible to gerrymander with ease. In theory past it has generally been held that redistricting happens every 10 years, so the middle of every third president.