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We're having the third SoCal LessWrong meetup this Saturday, the 23rd. It'll be held at this IHOP in Irvine, from 1PM to 8PM, in the upstairs meeting area.
For those that haven't yet come, the last two were quite successful bringing 13 and 16 people respectively, and there was plenty of intelligent and friendly discussion.
Make sure to comment if you have suggestions for how to improve on the last one, if you can give/need a ride, or just to say you're coming.
Suppose I hand you a series of data points without providing the context. Consider the theory v = a*t for t<<1, v = b for t>>1. Without knowing anything a priori about the shapes of the curves, one must have enough data to make sure that v follows the right lines at the two limits since there is complexity that must be justified. Here we have two one-parameter curves, so we need at least two data points to pick the right slope and offset, as well as at least a couple more to make sure it follows the right shape.
This is what I’ll call a completely local theory – see data, fit curve. Dealing with problems at this level does not leave much room for human bias or error, but it also does not allow for improvement by including background knowledge.
The majority of people would hold more accurate beliefs if they simply believed the majority. To state this in a way that doesn't risk information cascades, we're talking about averaging impressions and coming up with the same belief.
To the degree that you come up with different averages of the impressions, you acknowledge that your belief was just your impression of the average, and you average those metaimpressions and get closer to belief convergence. You can repeat this until you get bored, but if you're doing it right, your beliefs should get closer and closer to agreement, and you shouldn't be able to predict who is going to fall on which side.
Of course, most of us are atypical cases, and as good rationalists, we need to update on this information. Even if our impressions were (on average) no better than the average, there are certain cases where we know that the majority is wrong. If we're going to selectively apply majoritarianism, we need to figure out the rules for when to apply it, to whom, and how the weighting works.
This much I think has been said again and again. I'm gonna attempt to describe how.
Unfortunately, we are kludged together, and we can't just look up our probability estimates in a register somewhere when someone asks us "How sure are you?".
The usual heuristic for putting a number on the strength of beliefs is to ask "When you're this sure about something, what fraction of the time do you expect to be right in the long run?". This is surely better than just "making up" numbers with no feel for what they mean, but still has it's faults. The big one is that unless you've done your calibrating, you may not have a good idea of how often you'd expect to be right.
I can think of a few different heuristics to use when coming up with probabilities to assign.
1) Pretend you have to bet on it. Pretend that someone says "I'll give you ____ odds, which side do you want?", and figure out what the odds would have to be to make you indifferent to which side you bet on. Consider the question as if though you were actually going to put money on it . If this question is covered on a prediction market, your answer is given to you.
2) Ask yourself how much evidence someone would have to give you before you're back to 50%. Since we're trying to update according to bayes law, knowing how much evidence it takes to bring you to 50% tells you the probability you're implicitely assigning.
For example, pretend someone said something like "I can guess peoples names by their looks". If he guesses the first name right, and it's a common name, you'll probably write it off as fluke. The second time you'll probably think he knew the people or is somehow fooling you, but conditional on that, you'd probably say he's just lucky. By bayes law, this suggests that you put the prior probability of him pulling this stunt at 0.1%<p<3%, and less than 0.1% prior probability of him having his claimed skill. If it takes 4 correct calls to bring you to equally unsure either way, then thats about 0.03^4 if they're common names, or one in a million1...
Response to: When (Not) To Use Probabilities
“It appears to be a quite general principle that, whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought.” —E. T. Jaynes
The uncertainty due to vague (non math) language is no different than uncertainty by way of "randomizing" something (after all, probability is in the mind). The principle still holds; you should be able to come up with a better way of doing things if you can put in the extra thought.
In some cases, you can't afford to waste time or it's not worth the thought, but when dealing with things such as the deciding whether to run the LHC or signing up for cryonics, there's time, and it's sorta a big deal, so it pays to do it right.
If you're asked "how likely is X?", you can answer "very unlikely" or "0.127%". The latter may give the impression that the probability is known more precisely than it is, but the first is too vague; both strategies do poorly on the log score.
If you are unsure what probability to state, state this with... another probability distribution.