Mr. Bonaccorsi:
Here are two links to classic posts by Eliezer Yudkowsky that you may find pertinent to the second dialog from your last comment. I hope you enjoy them.
Let's establish some notation first:
P(H): My prior probability that the coin came up heads. Because we're assuming that the coin is fair before you present any evidence, I assume a 50% chance that the coin came up heads.
P(H|E): My posterior probability that the coin came up heads, or the probability that the coin came up heads, given the evidence that you have provided.
P(E|H): The probability of observing what we have, given the coin in question coming up heads.
P(E&H): The probability of you observing the evidence and the coin in question coming up hea...
No, the chance that the kidnapped child is a boy is 1/2.
In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys.
In the correct version of the story, you do not gain access to any information that allows you to differentiate between the mathematician's two children and identify a specific child as a boy.
...A woman says, "I have two children." You respond, "What are thei
But why is the goal of voting an example important? For me, what matters is creating your own example, and helping those who put theirs.
I agree with you. Receiving votes on our posts and comments is only an instrument to help us build better content. The content and how people use it is what matters.
Although the karma voting system provides imperfect information, it provides cheap imperfect information. Separating the question and answer seems like an easy way to make better use of the information that the votes provide. One benefit that I see from the ...
rstarkov wrote a nice discussion piece on the two envelopes problem: Solving the two envelopes problem. thomblake commented that the error most people make with this problem is treating the amounts of money in the envelopes as fixed values when calculating the expectation.
Here's a solution to a more general version of the problem:
Let's say that the red envelope contains N times as much money as the blue envelope with probability p, and the blue envelope contains N times as much money as the red envelope with probability (1 - p).
Without loss of generality, N is at least 1.
If N = 1, both envelopes contain the same amount, and there is no point in switching.
If N > 1, let the variable s represent the smaller amount of money between the amounts of the two envelopes. So one envelope contains s, and the other envelope contain...
...[Political "gaffe" stories] are completely information-free news events, and they absolutely dominate political news coverage and analysis. It's like asking your doctor if the X-rays show a tumor, and all he'll talk about is how stupid the radiologist's haircut looks. . . . ["Blast"] stories are. . . just as content-free as the "gaffe" stories. But they are popular for the same reason: There's a petty, tribal satisfaction in seeing a member of our team really put the other team in their place. And there's a rush of outrage ad
instead of covering pending legislation or the impact it could have on your life
If "impact on your life" is the relevant criterion, then it seems to me Wong should be focusing on the broader mistake of watching the news in the first place. If the average American spent ten minutes caring about e.g. the Trayvon Martin case, then by my calculations that represents roughly a hundred lifetimes lost.
It's weird how proud people are of not learning math when the same arguments apply to learning to play music, cook, or speak a foreign language.
Please correct me if any of my assumptions are innacurate, and I apologize if this comment comes off as completely tautological.
Expected utility is explicity defined as the statistic
U(x)})
where X is the set of all possible outcomes associated with a particular gamble, p(x) is the proportion of times that outcome x occurs within the gamble, and U(x) is the utility of outcome x, a function that must be strictly increasing with respect to the monetary value of outcome x.
To reduce ambiguity:
1A, 1B, 2A, and 2B are instances of gambles.
For 1B, the possible o
Hello. I'm William. I am a thirty year-old undergraduate student in the University of Wisconsin--Madison's Industrial and Systems Engineering department, with some additional study in Computer Science.
The study of logic and rational thought have always been hobbies of mine. My interest in mathematical optimization techniques has also been developing for decades, but this interest in these dark arts started taking steroids when I realized simple ways to apply the techniques to video games and Poker.
I originally stumbled upon this site two years ago, while ...
"Your dirty lying teachers use only the midnight to midnight 1 day (ignoring 3 other days) Time to not foul (already wrong) bible time."