The fundamental problem I have with all of this kind of analysis is that it treats democracy as a tool for finding the median set of ideas amongst a population of people with ideas, and that the “most democratic” system would enact the idea of each idea set that is most tolerable to the most number of people. This is the ur-liberalism.
Politics is the process by which society’s scarce resources (commodities, nature, leisure, whatever) are allocated between people with competing interests. A just outcome would require negotiation between representatives of affinity groups, however composed and however determined, weighted somehow by the size of each group and the impact upon them. Matters of popular opinion just fundamentally are not the problem of politics, and the Condorcet criterion is only good for finding the least unpopular opinion.
I honestly think there’s just no way to make a single-seat election just or democratic in any meaningful way. Multi-member districts are better, since at least you might elect representatives from multiple affinity groups.
Liberalism is “the ideology of capitalism,” of course, but also all the stated beliefs about individual freedom, one man one vote, self-determinism, everything that makes westerners feel warm and squishy. I believe all of this is ultimately based in idealism; in a fundamental belief that society progresses through the competition of ideas, and that the best ideas win out when they are explained to the masses. The search for the best voting system seems like the search for the final proof that society really can be improved one good idea at a time.
Rather than, you know, reckoning that the history of politics is the history of class struggle.
So starting with the assumption that people who want to build a hospital negotiated for the resources to be diverted to build exactly one hospital (in today’s world: they got a grant from the feds):
Voting obviously isn’t where we start; if each individual has a different idea of where to build the hospital there’s nothing to vote on.
Influential individuals might put forth ideas or arguments as to where to put the hospital, and they might collect others around them and organize for their preferred location. Maybe opinion coalesces around two locations, A and B. We now have two affinity groups, who have decided they have a collective interest in each of those locations, with people making any number of individual negotiations to land themselves in those groups.
The politics happened when people organized themselves into groups and decided on their interests. Ideally, the final decision would involve a negotiation between these groups (hospital goes to A, but with a tram line to the largest neighborhood near B, or whatever).
This isn’t really very different than how it works now, except now the groups wouldn’t usually have any public involvement since most people intuitively understand that they have no political relevance. Some capitalist who wants A will direct their lobby group to ask that of officeholders, maybe capitalist B also exists, maybe others if they don’t get scared off by the competition. The officeholders don’t generally have any personal interest in the outcome—they aren’t members of either group in our example—but they have interests in keeping various lobby groups happy and might negotiate with them on those terms. The point is that the political negotiations always happen.
The final voting on A or B, if it happens, is just a formality. Even if we had direct democracy the process to get to those two was much more impactful, and only the really interested would come out to vote anyway, making it again mostly a formality. If you could force every person to have an informed opinion on A or B, and then force them all to vote, then certainly the result would be meaningful… but this comes back to exactly my point about idealism.
Ultimately my point here is that matters of public political opinion only exist in the kind of mathematical models used to evaluate different voting systems. All real politics is negotiation, and finding the best voting system is irrelevant.