RobinZ comments on Open Thread: April 2010 - Less Wrong

4 Post author: Unnamed 01 April 2010 03:21PM

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Comment author: RobinZ 07 April 2010 03:56:53AM 0 points [-]

Oh, and then there are the times when you'll give different probabilities for the same event, if the question is worded in different ways.

That implies a very easy Dutch-book:

  1. Create a lottery with three possible outcomes (a), (b), and (c) - for example, (a) 1, (b) 2, 3, or 4, and (c) 5 or 6 on a six-sided die. (Note that the probabilities are not equal - I have no need of that stipulation.)

  2. Ask "what are the odds that (a) will happen?" In response to the proposed even-odds, bet against (a).

  3. Ask "what are the odds that (b) will happen?" In response to the proposed even-odds, bet against (b).

  4. Ask "what are the odds that (c) will happen?" In response to the proposed even-odds, bet against (c).

  5. Collect on two bets out of three, regardless of outcome.