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Kingreaper comments on Human inability to assign numerical probabilities - Less Wrong Discussion

2 Post author: AlexMennen 30 September 2010 04:42AM

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Comment author: Kingreaper 23 October 2010 11:19:27AM 0 points [-]

I find the idea of having a range of probabilities sensible.

If you give a single probability, all you tell someone is your expectation of what will happen.

If you give a probability range you're transmitting both your probability AND your certainty that your probabiliy is correct; IOW (In Other Words) you are telling the listener how much evidence you believe yourself to have.

So, as you gain more evidence your probability range will narrow.

Comment author: Kingreaper 23 October 2010 12:17:05PM 0 points [-]

To clarify:

When you find a probability through bayes-fu, you need a prior. Precisely one prior. Which is going to be pretty arbitrary.

But what if you picked two symmetrical priors, and applied the evidence to those? You start with prior 1: 99.99% Prior 2: 0.01%

When you have a reasonable amount of evidence you'll find that prior 1 and prior 2 result in similar values (ie. prior 1 might give 40% while prior 2 gives 25%) If you were to get more evidence, the difference would gradually vanish, and the smaller the probability range the more firm your probability is.