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Locaha comments on Polling Thread - Less Wrong Discussion
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Comments (118)
All the information you can gain from them factors through "the opinions of the population that takes the poll".
If you poll people about the likelihood of pixies, I guess you can learn something about their beliefs. You will learn nothing about pixies, though.
Well, people are more likely to believe in pixies in worlds with pixies than in worlds without pixies. It's just that your prior is so low that even the posterior will be negligible.
As long as their beliefs aren't totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts. Thus learning their beliefs would be informative about pixies.
Learning their beliefs would be informative about something.
Do a mental experiment, replace pixies with Jesus.
Learning people's beliefs about Jesus is informative about Jesus, it's just you already know that a lot of people believe in Jesus so there's very little new information.
Do you dispute the truth of the sentence that precedes the one you quoted? Here it is again: "As long as their beliefs aren't totally independent of the facts, those beliefs will constitute evidence (one way or the other) of the facts."
Replacing "pixies" with "Jesus" should not change whether people's beliefs are informative about Jesus. It may change the degree to which their beliefs are informative, for the reason /u/RowanE mentioned.
I am not suggesting that learning people's beliefs about pixies would be incredibly informative. I am only suggesting that it would be more informative than not learning about such beliefs.
Here's a thought experiment I often find helpful, tailored to the pixie-belief question:
If your answer is no, then we can conclude that you really do consider people's pixie-beliefs to be completely devoid of information about the reality of pixies. But if you would open the envelope, can't we conclude the opposite: that you consider their beliefs to be entangled with the truth, however tenuously?
(I like this thought experiment because in the past it has helped me see when I am believing in belief instead of, as I had supposed, just believing. I think I starting doing it after reading this 2011 Yvain post.)
That's because I already have strong opinions about pixies. If I polled people about something which they knew well and I knew badly, then I would learn something about whatever it was.
Should probably distinguish between voluntary-response and randomly sampled polling...
I answered "no" assuming that "the population that takes the poll" means literally "the people that take the poll". I probably would have answered "yes" had I considered it to mean "people similar to the people that take the poll (in some relevant way or ways)".
You may have missed the word almost. :-)
No “I don't know” answer?