RobinZ comments on The Prediction Hierarchy - Less Wrong

21 Post author: RobinZ 19 January 2010 03:36AM

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Comment author: PhilGoetz 19 January 2010 05:54:49AM 5 points [-]

Why, when you consider the case where you calculated the odds of winning the lottery incorrectly, do you increase rather than decrease the odds?

In any case, with a lottery, you do know the odds of winning; they're stated on the ticket.

Comment author: RobinZ 19 January 2010 12:52:43PM *  1 point [-]

Edit: I see I misread the remarks. See downthread.

At the moment, I'm calculating my expected value, not the odds, but there are a number of reasons to think that jackpot / stated-odds is optimistic:

  1. The lottery may be a fraud.

  2. The lottery may go bust.

  3. I may lose the ticket.

  4. I may have to split the pot.

In general, the rigorous approach would be to rewrite everything as probability distributions.

Besides: if you want to assume the average lottery ticket is more valuable that I would - e = -0.5*t, say - that's your right. I make no justification for my priors.

Comment author: PhilGoetz 19 January 2010 08:36:49PM 2 points [-]

You quoted this from somewhere:

According to your calculations, "this ticket will not win the lottery" is true with probability 99.9999975%. But can you really be sure that you can calculate anything to that good odds? Surely you couldn't expect to make forty million predictions of which you were that confident and only be wrong once. Rationally, you ought to ascribe a lower confidence to the statement: 99.99%, for example.

This says that rationally, you should assign a much higher expected value to the ticket. But all 4 factors you just listed are ones which would make the expected value of the ticket lower.

Comment author: RobinZ 19 January 2010 09:50:46PM *  0 points [-]

Oh, I see what you mean. That wasn't a quote, actually - it was essentially an articulation of ciphergoth's clever (but incorrect) argument. The purpose of this post was to explain my method for rebutting it.

Comment author: ciphergoth 19 January 2010 11:09:16PM 1 point [-]

It's just a restatement of the Pascal's Mugging problem, but with the lottery in place of the mugging.

Comment author: RobinZ 20 January 2010 01:57:08AM 1 point [-]

I'm still ambivalent about Pascal's Mugging, however - my instinct is to refuse to pay, but I don't feel I can sufficiently justify that response.

The lottery, as an ordinary situation, is far more tractable.

Comment author: ciphergoth 20 January 2010 07:59:52AM 1 point [-]

Can't you apply a similar argument? Instead of considering P(mugger's statement is true), you consider P(you have the faintest idea what's going on).

Comment author: RobinZ 20 January 2010 12:53:52PM 0 points [-]

My instinctive probability measurement for such a statement is not so small as 1/3^^^^3. My best retort at the moment is purely pragmatic: never accept such a mugging, because otherwise you will be mugged.

Comment author: ciphergoth 20 January 2010 01:00:10PM 0 points [-]

Indeed, the probability that we don't know what's going on is non-negligible. What I'm suggesting is that we don't have to assign a non-negligible probability to the specific hypothesis "this mugger is speaking the literal truth" - instead we avoid overconfidence by trying to consider all of the hypotheses that might hide behind the general assertion "our grasp on this situation is much less than we think" and try to use broader reference classes to see what the outcomes of various strategies might be in those instances, using the strategy you outline for the lottery.

Comment author: RobinZ 20 January 2010 01:24:12PM 0 points [-]

Not to engage in needless turnabout, but how does that translate into math?

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