> There are all kinds of geographical and legal boundaries in a country, with varying levels of affinity to them. Defining gerrymandering precisely isn't possible, it isn't even a know it when you see it thing ...
One way to define the problem is to maximize the number of competitive elections.
Hmm, okay, so what would be fair? Perhaps we want to give each party a fighting chance in each election? Isn't that fair?
2 districts each hold 100,000 blues
8 districts hold 50,000 blues and a 50,000 violets
So now the violets have a 50% chance of winning 8 districts. The blues are granted two districts automatically, but that is fair, since they are more popular than the violets. Each party has some chance of winning.
However, in this model, if 1 blue voter in each district changes their mind, then the violets end up with 80% of the legislature. We’ve engineered a system that is very unstable! If Katechon is like the nation of Hungary, where a 2/3rds majority can amend the constitution, then Katechon is now vulnerable to an authoritarian takeover, much like what happened in Hungary after 2010. And that's because 8 people out of a 1,000,000 changed their vote.
Interesting idea. Mathematically it seems that it would on average create a perfect distribution. But it'd also lend itself to some substantial variance.
Imagine you have a 650-350 voter lead in a state with 10 districts. The way you maximize the number of competitive election is by packing 3 districts 100-0. The party with 650 voters now has the same number of voters remaining as the party with 350, for the next 7 districts.
Mathematically this works out perfectly because the party with 650 voters has an overall seat expectation of (3 + 7 * 0.5) = 6.5, but if you run the math further here's how it looks. The party with 35% of the representation gets (assuming a 50% outcome per competitive election):
One way to define the problem is to maximize the number of competitive elections.