No, why? Arrow's Theorem eg has nothing to say about proportional representation. And Arrow's Theorem only applies to aggregating orderings of a finite list of preferences. But the methods under investigation need to be 'generic', ie can't make use of any special properties of those preferences, either. (See eg https://people.mpi-sws.org/~dreyer/tor/papers/wadler.pdf for how being 'generic' limits what your methods can do.)

And to come back to iterated games: almost no matter how the representative was chosen in the first period, if she's standing for re-election, she has an incentive for keeping her represented happy.

Arrow's theorem just applies to a list of static choices; not to how the chosen might behave when trying to get re-elected.

> Have you seen literature on this somewhere?

I don't remember right now. But I think 'The Myth of the Rational Voter' might mention some research somewhere. (See https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter) That book mostly mentions this when it argues that the problem with democracy ain't that voters don't get their wishes, but the problem is that voters do get their wishes.

> Whereas it's pretty darn easy to see how the candidate who promised you tax breaks suddenly voted to raise them when he came into office.

Sure. But if millions of people are eligible to be drafted at random, you are going to have a hard time pre-emptively bribing them. That's equivalent to doing something nice for the entire country.

> I see nothing obvious suggesting that your (homemade?) scheme is better, so I'm gonna put the onus on you to explain it wouldn't suffer from similar problems...

Because eg people who don't want to stand for parliament still have a say? That was exactly one of the problem you brought up with naive sortition. Remember?

> Note that "theorem assumptions don't apply" doesn't imply "conclusion doesn't hold".

Well, if your theorem says A implies B; if A doesn't hold, your theorem doesn't apply, but B could still be true for other reasons. But you need a different argument or empirical data to convince people of B.