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Jayson_Virissimo comments on Is my view contrarian? - Less Wrong
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Garth Zietsman, who according to himself, "Scored an IQ of 185 on the Mega27 and has a degree in psychology and statistics and 25 years experience in psychometrics and statistics", proposed the statistical concept of The Smart Vote , which seems to resemble your "Mildly extrapolate elite opinion". There are many applications of his idea to relevant topics on his blog.
It's not choosing the most popular answer among the smart people in any (aggregation of) poll(s), but comparing the proportion of the most to the less intelligent in any answer, and deciding The Smart Vote is that which has the largest ratio, after controlling for possible interests.
J. S. Mill had a similar idea:
-- Wilson, Fred, "John Stuart Mill", The Stanford Encyclopedia of Philosophy
There is nobody who I'd trust to decide who is considered educated and more responsible and therefore who would get more votes. And the historical record on similar subjects is pretty bad.
I would also expect a feedback loop where people who can vote more vote to give more voting power to people like themselves.
(And I also find it odd that most people who contemplate such things assume they would be considered educated and more responsible. Imagine a world where, say, the socially responsible get more voting power, and that (for instance) thinking that there are innate differences between races or sexes disqualifies one from being socially responsible.)
The pervasive influence of money in politics sort of functions as a proxy of this. YMMV for whether it's a good thing...
Even though he calls it "The Smart Vote", the concept is a way to figure out the truth, not to challenge current democratic notions (I think), and is quite a bit more sophisticated than merely giving greater weight to smarter people's opinions.