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gwern comments on 2011 Survey Results - Less Wrong
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You have to admit, that's pretty awful. There's only a 20% difference, is that so?
Note that the top 25% put 99 or above for Universe. Of those, I would be surprised if there weren't a big chunk that put 100 (indicating 100 - epsilon, of course). This is not weighed in appropriately. Likewise for the bottom 25% for Galaxy.
Basically, "If you hugely truncate the outside edges, the average probabilities wind up too close together" should be entirely unsurprising.
Percentage point difference in belief probability isn't all that meaningful. 50% to 51% is a lot smaller confidence difference than 98% to 99%.
69.4% probability means 3.27 odds; 41.2% probability means 1.70 odds.
That means that, in the aggregate, survey takers find (3.27/1.70) = 1.924 -> 0.944 more bits of evidence for life somewhere in the universe, compared to somewhere in the galaxy.
Is that unreasonably big or unreasonably small?
EDIT: Oops, I can't convert properly. That should be 2.27 odds and 0.70 odds, an odds ratio of 3.24, or 1.70 more bits.
If we take the odds ratio for each individual respondent (instead of the aggregate), the median odds ratio is 10.1 -> 3.3 more bits of evidence for life in the universe, compared to somewhere in the galaxy. 25th percentile odds ratio: 2.7 -> 1.4 more bits; 75th percentile odds ratio: 75.7 -> 6.2 more bits. (This is all using the publicly available data set; looking at the aggregate in that data set I'm getting an odds ratio of 3.6 -> 1.8 more bits.)
People who believe in God/religion/the supernatural tend to give a lower odds ratio, but other than that the odds ratio doesn't seem to be associated with any of the other variables on the survey.
I'm not comfortable with bit odds, especially in this context, so I dunno. How would you frame that in the opposite terms, for lack of existence?
That gives .44 odds non-existence in universe, 1.43 odds non-existence in galaxy, a ratio of 3.24, or 1.70 more bits of evidence for no (non-human) life in the galaxy compared to the universe in general.
And I forget why those two answers are allowed to be different...
EDIT: I made an error in the first calculation; as I suspected, the values are symmetric.
Fear not! The 28% difference in the average meaningless. The difference I see in that quote is (90-30), which isn't nearly so bad - and the "1" is also rather telling. More importantly by contrasting the averages with the medians and quartiles we can get something of a picture of what the data looks like. Enough to make a guess as to how it would change if we cut the noise by sampling only, say, those with >= 200 reported karma.
(Note: I am at least as shocked by the current downvote of this comment as gwern is by his "20%", and for rather similar reasons.)
I had the same reaction. The only defense I can imagine is that the second proposition is "in our galaxy" and not "in a random galaxy" - before looking, we should expect to find more other intelligent species in ours, which we know at least doesn't rule out the possibility :)
I tried to guess how many our-galaxy intelligent-life-expectation equivalents exist in our universe. I personally find 50 (the 25% quartile) laughably low.
1:50 and (100-99):(100-80) are fairly extreme - just not extreme enough.
"20% difference" between what and what?
The point being that if there is intelligent life elsewhere in the universe and it hasn't spread (in order to maintain the Great Silence), then the odds of our 1 galaxy, out of the millions or billions known, being the host ought to be drastically smaller even if we try to appeal to reasons to think our galaxy special because of ourselves (eg. panspermia).
If the strong filter is propagation through space, then for rates which people could plausibly assign to the rate of occurrence of intelligent life, the probabilities could be near identical.
What are the odds that a randomly selected population of 10000 has any left handed people? What are the odds that an entire country does?
Ditto if the strong filter is technological civilization (which strikes me as unlikely, given the anthropological record, but it is one of the Drake terms). If there are ten thousand intelligent species in the galaxy but we're the only one advanced enough to be emitting on radio wavelengths, we'd never hear about any of the others.
Such a set of probabilities may be justified if you're very uncertain (as seems superficially reasonable) about the baseline probability of life arising in any given galaxy. So perhaps one might assign a ~40% chance that life is just incredibly likely, and most every galaxy has multiple instances of biogenesis, and a ~40% chance that life is just so astronomically (har har har) improbable that the Earth houses the only example in the universe,
This is almost certainly much less reasonable once you start thinking about the Great Filter, unless you think the Filter is civilizations just happily chilling on their home planet or thereabouts for eons, but then not everybody's read or thought about the Filter.
I was kind of hoping most LWers at least had heard of the Great Silence/Fermi controversy, though.
Maybe there should be a question or two about the Fermi paradox.
The bigger problem to me seems that both the numbers (galaxy and universe) are way too high. It seems like it should be more in the range of "meta-uncertainty + epsilon" for both answers. Maybe "epsilon * lots" for the universe one but even that should be lower than the uncertainty component.