I presume you're saying that utility-based simulations are not credible, because they're clearly numerical estimates.
Actually, no, that's not what I mean. I have no problems with numerical estimates in general.
What I mean by "credible", in this context, is "shown to be relevant to real-life situations" and "supported by empirical data".
You've constructed a model. You've played with this model and have an idea of how it behaves in different regimes. That's all fine. But then you imply that this model reflects the real world and it's at this point that I start to get sceptical and ask for evidence. Not evidence of how your model works, but evidence that the map matches the territory.
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Democracy is complicated. For a simple example, consider full direct democracy: instant whole-population referendums on every issue. I am not sure anyone considers this a good idea -- successful real-life democratic systems (e.g. the US) are built on limited amounts of democracy which is constrained in many ways. Given this, democracy looks to be a Goldilocks-type phenomenon where you don't want too little, but you don't want too much either.
And, of course, democracy involves much more than just voting -- there are heavily... entangled concepts like the rule of law, human rights, civil society, etc.
Full direct democracy is a bad idea because it's incredibly inefficient (and thus also boring/annoying, and also subject to manipulation by people willing to exploit others' boredom/annoyance). This has little or nothing to do with whether people's preferences correlate with their utilities, which is the question I was focused on. In essence, this isn't a true Goldilocks situation ("you want just the right amount of heat") but rather a simple tradeoff ("you want good decisions, but don't want to spend all your time making them").
As to the other related concepts... I think this is getting a bit off-topic. The question is, is energy (money) spent on pursuing better voting systems more of a valid "saving throw" than when spent on pursuing better individual rationality. That's connected to the question of the preference/utility correlation of current-day, imperfectly-rational voters. I'm not seeing the connection to rule of law &c.