It would require a more fundamental recognition of political parties than the constitution provides.

Gerrymandering is not a technological problem.

Unfortunately, given Duverger's law [0], first past the post electoral systems eventually resolve into two party systems.

Essentially, in a first past the post system, voting for any other candidate other than the one both most likely to win AND whose politics most closely aligns with your own is effectively a vote for the major party candidate who least aligns with your politics.

[0] https://en.wikipedia.org/wiki/Duverger%27s_law

edit for link.

Why can't you just split elected representatives into two groups, regardless of stated political affiliation? One group then cuts, the other chooses.

Defections. Electeds will happily maximize their own personal power at someone else's expense. There are many examples of getting opposition support for inequity in exchange for safe seats.

People outside of (partisan) politics don't often get to see that the party orgs and the politicians are usually in conflict. More so on the left than on the right.

Interestingly enough, this works even for defectors. They still have to participate in a turn-based game against a competitor.

There is a whole field of study around efficient "cake cutting" algorithms, many of which contemplate and account for defectors.

https://en.wikipedia.org/wiki/Fair_cake-cutting

I've been trying to dream up ways to use general purpose strategies like this to mitigate regulatory capture. Applicable to two party systems with no clear obvious third party to forge a balance of powers, a durable trilemma.

There are fair algorithms for multi-way division... but yeah, it's going to be real hard for a third party to break in when the two ruling parties can conspire to block them.

Ah that's very clever, like when my sister and I split a candy bar in grade school. It really worked then as it would now.