Simetrical
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The question required us to provide real numbers, and infinitesimals are not real numbers. Even if you allowed infinitesimals, though, 0 would still be the Nash equilibrium. After all, if 1/∞ is a valid guess, so is (1/∞)*(2/3), etc., so the exact same logic applies: any number larger than 0 is too large. The only value where everyone could know everyone else's choice and still not want to change is 0.
Doing this with server side scripting is crazy. You'd have to submit a zillion forms and take a second to get the answer for each try. This is precisely the sort of thing client-side scripting is meant for.
Of course, the page would explain that it needed JavaScript, if you had JavaScript disabled, not just show a blank page.
I got the wrong rule, but it said I was right because I made only one mistake. I thought the rule was that a sequence was awesome if it was an increasing arithmetic progression. The only one of your examples at the end that contradicted this was 2, 9, 15. All the other awesome ones were, in fact, increasing arithmetic progressions: five out of the six awesome sequences you gave at the end. You should probably cut that down to two or three, so I'd have lost.
That clears things up a lot. I hadn't really thought about the multiple-models take on it (despite having read the "prior probabilities as mathematical objects" post). Thanks.
Even accepting the premise that voting for the proposition was clearly wrong, that's a single anecdote. It does nothing to demonstrate that Mormons are overall worse people than atheists. It is only a single point in the atheists' favor. I could respond with examples of atheists doing terrible things, e.g., the amount of suffering caused by communists.
Anecdotes are not reliable evidence; you need a careful, thorough, and systematic analysis to be able to make confident statements. It's really surprised me how commonly people supply purely anecdotal evidence here and expect it to be accepted (and how often it is accepted!). This is a site all about promoting... (read more)
I think this post could have been more formally worded. It draws a distinction between two types of probability assignment, but the only practical difference given is that you'd be surprised if you're wrong in one case but not the other. My initial thought was just that surprise is an irrational thing that should be disregarded ― there's no term for "how surprised I was" in Bayes' Theorem.
But let's rephrase the problem a bit. You've made your probability assignments based on Omega's question: say 1/12 for each color. Now consider another situation where you'd give an identical probability assignment. Say I'm going to roll a demonstrated-fair twelve-sided... (read more)
I see this conclusion as a mistake: being surprised is a way of translating between intuition and explicit probability estimates. If you are not surprised, you should assign high enough probability, and otherwise if you assign tiny probability, you should be surprised (modulo known mistakes in either representation).
That's not true at all. Before I'm dealt a bridge hand, my probability assignment for getting the hand J♠, 8♣, 6♠, Q♡, 5♣, Q♢, Q♣, 5♡, 3♡, J♣, J♡, 2♡, 7♢ in that order would be one in 3,954,242,643,911,239,680,000. But I wouldn't be the least bit surprised to get it.
In the terminology of statistical mechanics, I guess surprise isn't caused by low-probability microstates... (read more)
Huh. Do you need me to post a few dozen links to articles detailing incidents where Mormons did evil acts because of their religious beliefs? I mean, Mormonism isn't as inherently destructive as Islam, but it's not Buddhism either.
Do you have empirical evidence that Mormons are more likely to cause harm than atheists? (Let's say in the clear-cut sense of stabbing people instead of in the sense of spreading irrationality.) Mormons might do more bad things because their god requires it, but atheists might do more bad things because they don't have a god to require otherwise. They might be more likely to become nihilists or solipsists and not... (read more)
If the question is "Should Wednesday, while not exactly choosing to believe religion, avoid thinking about it too hard because she thinks doing so will make her an atheist?," then she's already an atheist on some level because she thinks knowing more will make her more atheist, which implies atheism is true. This reduces to the case of deception, which you seem to be against unconditionally.
That's not necessarily true. Perhaps she believes Mormonism is almost certainly right, but acknowledges that she's not fully rational and might be misled if she read too many arguments against it. Most Christians believe in the idea that God (or Satan) tempts people to sin,... (read more)
In that case Warrigal would have said "rational" rather than "real". Numbers such as 17π would presumably be fine too, not just fractions. "No funny business" presumably means "I'd better be able to figure out whether it's the closest easily". For instance, the number "S(12)/2^n, where S is the max shifts function and n is the smallest integer such that my number is less than 100" is technically well-defined, in a mathematical sense. But if you can actually figure out what it is, you could publish a paper about it in any journal of computer science you liked.