I think there's a lot of interesting potential in such ideas - but that this isn't ambitious enough! Democracy isn't just about compromising on the issues on the table; the best forms involve learning more and perhaps changing our minds... as well as, yes, trying to find creative win-win outcomes that everyone can at least accept.

I think that trying to improve democracy with better voting systems is fairly similar to trying to improve the economy with better price and capital-allocation sytems. In both cases, there have been enormous advances since the mid-1800s; in both there's a realistic prospect of modern computers enabling wildly better-than-historical systems; and in both cases it focuses effort on a technical subproblem which not sufficient and maybe not even necessary. (and also there's the spectre of communism in Europe haunting both)

A few bodies of thought and work on this that I like:

• classic speeches, letters, and essays on citizenship, such as Citizenship in a Republic or Letter from a Birmingham Jail ("the books of the future would be just as good a corrective as the books of the past, but unfortunately we cannot get at them")
• consensus decision-making. I'm particularly familiar with and fond of the UCA Manual for Meetings; Beyond the Majority Rule gives a decent account of similar practices. Good practice feels like a large dance event; there's enough structure that you can all work together but not so much that you can't improvise when that'd work better.
• computer-enabled ideas like Polis (and relevantly e.g.) or the Collective Intelligence Project, The Computerization of Society (1978, France), arguably Alan Kay's Dynabook concept, Wikipedia and open source / open culture movements, ...

But as usual, the hard and valuable part is the doing!

I think there are a couple of interesting elements here.

1. Acknowledging that the individual AI representatives will act on preferences/values, there will be many situations where the optimal move is not what an individual person believes should be done.

Take a simple example. A large part (basically all?) of the US population wants cheap housing to be available, and for elite housing to be built in a value maximizing way (aka the elite want to get their money's worth). Yet a common preference is "no new housing built near me, where the noise/traffic/sight will affect me. And "building new luxury housing won't lower the market price for housing because demand is infinite". "Also I don't like seeing homeless people ".

What a person claims to want is opposed to how they want the government to act.

This also will make it difficult to audit ones AI representative. Decisions will become extremely complex negotiations.

2. If a single person's only voice is a vote, then for most issues the preferences of most voters don't matter. They can be ignored on the margin. This is because current democracy "bundles" decisions. Perhaps you had in mind a direct democracy where a person's ai representative votes on every decision.

If you can separate the how from the what, I wonder what people actually disagree on. An enormous amount of political conflicts seem to be disputes over the how, where people cannot agree on what policy has the highest probability of achieving a goal.

This is essentially just human ignorance: given a common data set about the world, you cannot agree to disagree: there is exactly one optimal policy using the rational policy that at that instant in time which has the highest EV (measured by back testing etc)