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Alsadius comments on [QUESTION]: What are your views on climate change, and how did you form them? - Less Wrong
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In a very handwavey sense. Voters are not, strictly speaking, IID. But it works out pretty similarly. I find that politically active folks(whether seriously or casually) mostly tend to care passionately about certain issues, but the actual election results are vastly smoother.
I don't think this comparison works at all. Not only the voters are not IID, but the actual election results are a discrete outcome and there is nothing "vastly smoother" about them. The political process is full of threshold functions.
Oh, certainly. But the overall motion is much less than one might think. A real blowout defeat of a party in the US is getting 45% of the vote to your opponent's 54%. Most countries are similar, if with more parties. The government swings, but voters as a whole don't do so too heavily.
So you are saying that the political views of populations are largely stable. Sure. But what does it have to with either democracy or the Central Limit Theorem?
Not just stable. Moderate, rarely obsessed with single issues, and in retrospect they're usually pretty good at making wise decisions on the broad strokes(even if they're bad at micropolicy - which makes sense, because so few people care about it). It's for the same reasons as the CLT, which is why I named it - the distinguishing characteristics and individual madnesses of voters cancel each other out, and you're left with a signal whose characteristics are defined by broad statistical characteristics, and not the quirks of a small group.