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Notes -
This sounds rather like the "wisdom of crowds" argument — or at least adjacent to it. But, AIUI, that only really applies when the "noise" is unbiased; like in the classic "guess how many items in the jar," the average of people's "noisy" estimates converges toward the true value because people are equally likely to overestimate as underestimate. Does that still apply in voting? I think a case can be made that for various reasons — ranging from human cognitive biases to media institutions — the "noise" is not unbiased; the average "dumb voter" will tend to deviate from the "true signal" in particular directions, ensuring the aggregate "wisdom of the crowd" will be similarly biased away from the "true signal" in those same directions.
That is probably the largest falsifiable assumption underlying the rationale, that the noise is not normally distributed around the true signal.
The truest answer is 'that is possible and is a major weakness of the theory,' but, 3 mitigating arguments:
We have a 2-party system, in which each side has arguments and narratives trying to push people towards their direction. Voting simulations tend to suggest that in this situation, or even situations with 3 or 4 parties, it is natural for those opposing parties to center around the true center of public preference, and pull in either direction away from it. Since both parties have roughly similar number of devotees (which is not coincidental, they will change their positions until that equilibrium is reached in the long-run, which is part of why it centers that way in real life), we can expect/hope that the noise produced by those things roughly cancels out. (of course this conflates 'central voter preference' and 'the best government', but that gets into deeper philosophical discussions of what a 'good government' even is, which we're eliding atm)
Even if the population has net biases where everyone/the large majority are off in the same direction, these should be for specific issues or domains. Government is hugely complex and multi-faceted; it's possible for the government to be bad on 5 axes, ok on 10 axes, and good on 20 axes, or w/e. Even if there's some big universal bias that drives people away from the true signal on on axis or another, hopefully any axis without a singular such factor will still have pretty randomly distributed noise, and we'll do well on a lot of other metrics anyway.
In particular, I was comparing universal voting to some type of restricted voting where (for example) only people with a certain IQ or passing a certain competence test or etc. are allowed to vote. While it may be true that the general population of all voters could be systematically biased in some way, it's still much more likely that a smaller group selected on a specific metric, which therefore has less cognitive and experiential diversity, would have a similar or stronger bias of some kind. If you are trying to avoid systematic biases, it's really hard to do better than huge random samples in a situation like this, even if huge random samples aren't guaranteed to be perfect either. (and ofc I personally don't think you're going to do better hoping to get lucky with a benevolent monarch or any other system humans have tried, but maybe better non-voting systems are theoretically possible)
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