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army1987 comments on 2012 Survey Results - Less Wrong
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In the fair coin questions, there were two people answering 49.9, one 49.9999, one 49.999999, and one 51. :-/
Here is a paper which shows that natural coin tosses are not fair- with a 51:49 bias of the side thats "up" at the beginning. Maybe ask for the probability on an indealized coin toss next year? edit: fixed the markup
(For the
[text](url)link syntax to work, you need the full URL, i.e. including the http:// bit at the start: http://comptop.stanford.edu/preprints/heads.pdf)Certain tossing techniques can bias the results much more than that, as described in Probability Theory by Jaynes. But the survey did ask about a “fair coin” (emphasis added).
Were they excluded from the probabilities questions?
It was stated that they should give the obvious answer and that surveys that didn't follow the rules would be thrown out... but maybe 50% isn't as obvious as 99.99% of the population thinks it is.
Is there any reason the prompt for the question shouldn't have explicitly stated "(The obvious answer is the correctly formatted value equivalent to p=0.5 or 50%)"?
My working theory is that they were trolling.
Either way, should we or shouldn't we have trusted the rest of their answers to be statistically reliable?
I see no reason to throw out their responses. They appear to just not be familiar with the terminology. To someone that does not know that "fair coin" is defined as having .5 probability for each side, they might envision it as a real physical coin that doesn't have two heads.