felipec
unbelief
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User ID: 1796
felipec
unbelief
2yr ago
If you have a distribution over a probability of an outcome, it's entirely valid to integrate over that density and get a single number for the probability of the outcome.
You get the probability that the actual probability is on that region, but it's never 100%.
In fact, this works for any parameter: If you have a probability distribution Y for the mean of a random variable X with standard deviation 1, for example, then you can compute the average value of X.
But the average value is not necessarily "the answer".
felipec
unbelief
2yr ago
It's reasonable to express uncertainty, but for a case like this with a very limited set of possible outcomes then "I don't know" should still convert to a number.
No, it's a function, not a single number.
In fact, with maximum uncertainty, 50% is correct: If your distribution over the true probabilities is uniform, then integrating over that distribution gives your subjective probability of heads as 1/2.
No, if it's a uniform distribution you can calculate the probability that the actual probability is between 45% and 55%: 10%. For me 10% is very unlikely.
But the probability that the actual probability is between 90% and 100% is equally likely: 10%.
On the other hand, if you've flipped a lot of coins and you know that most coins are fair, then seeing 8 heads shouldn't move the needle much, so the answer might not be exactly 50% but it would be quite close.
You are confusing the most likely probability with "the answer". The most likely probability is close to 50%, yeah, but that's not the answer. The answer is a function. Given that function you can calculate the probability that the actual probability is between 45% and 55%, and given that the most likely probability is in this range, the likelihood is going to be high, but there's a non-zero probability that the true probability lies outside that range.
Probabilities of probabilities should make anyone question their own certainty on "the answer".
felipec
unbelief
2yr ago
The true problem with censorship is when it silences certain ideas. Child porn as he mentioned is not an idea, it's a red herring as nobody is truly arguing in favor of allowing that. The philosophical position that no ideas should be censored has been debated for centuries and it has a name: freedom of speech.
The problem is that today nobody really knows what freedom of speech actually is. The fact that moderation and censorship has been conflated is one problem, but so is the fact that the philosophical position has been conflated with the laws (First Amendment). It shows when people claim that freedom of speech is a right.
Freedom of speech was meant to safeguard heliocentrism, it wasn't meant to be a right of Galileo.
felipec
unbelief
2yr ago
Yes, and some Bayesians would even distinguish between e.g. 50% certainty in the coin landing heads on the next toss after 50 heads and 50 tails from your rational beliefs before testing the coin at all.
You can use the beta distribution to calculate the probability that the actual probability is between 45% and 55% given 50H/50T, and it's around 70%: graph. So in that case I would say I believe the coin is fair with 70% certainty. With 0H/0T it's around 10%.
The more tosses the more likely the actual probability is between a certain range, so the more "precise" it should be.
Articles from Stanford Encyclopedia of Philosophy are very interesting, but way too complicated for me. This article is no exception, very interesting, but my point is much more general.
By using probability I'm not trying to find an accurate value of belief, what I'm trying to do is show is that even in simple questions people have an unwarranted level of certainty, even people who call themselves "skeptics".
felipec
unbelief
2yr ago
Yes, but to point out what the true answer depends on, a level-3 skeptic has to first doubt the problem. A level-3 skeptic might not know the answer, but it's better to say "I don't know", than what some confident people would automatically say: 50%.
felipec
unbelief
2yr ago
I would put it as Hume did when discussing miracles: "A wise man proportions his belief to his evidence." Evidence is never conclusive, but it can be stronger or weaker.
Indeed. This is a point I often emphasize in debates. The quote "absence of evidence is not evidence of absence" is wrong because it is evidence, but people often confuse evidence with proof.
But I don't see evidence as a continuum, I see certainty as a continuum. I would say for example "I believe the coin is biased with 95% certainty". 50% certainty means no belief one way or the other. This is a matter of semantics of course.
In the end what "true skeptics" should agree is that 100% certainty is not characteristic of skepticism.
felipec
unbelief
2yr ago
"Beware, for not all who claim to be skeptics are ones."
Yes. Many people who claim to be skeptics actually are being skeptical in many claims, but the point of calling yourself "skeptic" is that you are being skeptical in all of them (or close to 100%). You can't call yourself a "peaceful" person if there are enough times you've reacted violently.
felipec
unbelief
2yr ago
Thank you. It would be helpful to state that to new users in the welcome message. I was told to "feel free to comment or post".
Actually you can't. I don't think you quite understand the point. I can program a
f()function that return headsppercent of the time. How many results do you need to accurately "calculate the probability of getting heads"?OK.
Yes, but the "expected value" is not "the answer".
I programmed your example of
0.3*0.4/0.7*0.7asg(0.3), let's say that the thresholdtin this case is 0.3, but I choose a different threshold for comparison and I run the function 10 times. Can you guess which results are which?[0.7, 0.4, 0.7, 0.7, 0.7, 0.7, 0.4, 0.7, 0.7, 0.4][0.7, 0.7, 0.7, 0.7, 0.4, 0.7, 0.7, 0.4, 0.7, 0.7]Which is
g(0.3), which isg(t), and what do you guess is the value oftI choose?More options
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