JGWeissman comments on Two probabilities - Less Wrong

1 Post author: rwallace 15 February 2010 02:18PM

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Comment author: JGWeissman 16 February 2010 12:15:27AM 1 point [-]

What probabilities do you assign to the following propositions?

  1. There is life on the northern hemisphere of Mars.
  2. There is life on the southern hemisphere of Mars.
  3. There is life on Mars.
Comment author: rwallace 16 February 2010 12:25:34AM 0 points [-]

Good example. I assign B = 0.5 in all three cases, but I expect the (unknown) value of F to be very similar (and close to 0 or 1) for all three, unlike in the case of three coin flips.

Comment author: JGWeissman 16 February 2010 12:41:51AM *  0 points [-]

Now, without using probabilities of 0 or 1, can you coherently assign probabilities to

A. 1 and 2
B. 1 and not 2
C. not 1 and 2
D. not 1 and not 2
Comment author: rwallace 16 February 2010 01:13:17AM 0 points [-]

Sure. B(A) = B(D) = 0.5, B(B) = B(C) = epsilon. (The 0.5 is only good to one significant figure, and even that's a stretch.)

Comment author: JGWeissman 16 February 2010 01:33:54AM 1 point [-]

Just how small is this epsilon? I might want to propose a bet.

Comment author: rwallace 16 February 2010 01:58:18AM 0 points [-]

If I had a number, I would've given the number instead of saying "epsilon" :) What's your proposed bet?

Comment author: JGWeissman 16 February 2010 02:19:47AM 0 points [-]

I might bet on B or C against A or D at odds of epsilon to 1, to be settled when we have thoroughly explored Mars, assuming that if there is life, we will find it. This of course depends on the actual value of epsilon.

Comment author: Lightwave 16 February 2010 01:10:49PM 0 points [-]

So basically you're saying that the probability of there being life on only one of the hemispheres is arbitrarily small?

Comment author: rwallace 16 February 2010 03:27:10PM 0 points [-]

Mathematically nonzero, but small enough that we can treat it as zero for practical purposes, yes.

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