LESSWRONG
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Olle50

Hold on, Johnicholas, isn´t there a slip in the calculation concerning the third reader, case 4? You say

  1. Low, one vote up and one vote down: (6:4)(4:1)(1:4)(14) = (6:1), vote up against judgement

...but shouldn't this produce the answer (3:8) rather than (6:1)? The conclusion seems to be that as long as either the score is tied or "down" leads by one, readers will keep on voting according to their judgement, while as soon as either "up" leads by one or "down" leads by one, the next reader and all the following will ignore their judgements and follow suit.

Slightly more complicated, but still a great example!

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7Johnicholas
You are ENTIRELY CORRECT! I am embarrassed and I apologize. I juggled the numbers repeatedly, trying to get a brief example that only uses numbers, not symbols; when it seemed like I had succeeded, I stopped. I'll think about how to correct the post.
Belief in Self-Deception
Olle20

topynate: It was only for reasons of space that I listed five events with probability 0.8 each, rather than 1000 events with probability 0.999 each; the modification is obvious.

Eliezer: Point taken.

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Belief in Self-Deception
Olle20

I judge each of the four teams to have probability 0.2 of winning the Champions League. Their victories are mutually exclusive. Hence I judge each of statements (1)-(5) to have probability 0.8.

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6topynate
Hm. Wittgenstein requires that the meaning be "indicative". In English the indicative mood is used to express statements of fact, or which are very probable. They don't necessarily have to be true or probable, of course, but they express beliefs of that nature. You say "I believe X" when you assign a probability of at least 0.8 to X; 0.8 is probable, but not very probable. Would you state baldly "Barcelona will not win the Champions League", given your probabilities? I doubt it. When you say instead "I believe Barcelona will not win the Champions League", you could equally say "Barcelona will probably not win the Champions League." But this isn't in the indicative mood, but rather in something called the potential/tentative mood, which has no special form in English, but does in some other languages, e.g. daro in Japanese (which has quite a complex system for expressing probability). It's better to just say your degree of belief as a numeric probability.
Belief in Self-Deception
Olle10

I believe the following five things.

(1) Barcelona will not win the Champions League.

(2) Manchester U will not win the Champions League.

(3) Chelsea will not win the Champions League.

(4) Liverpool will not win the Champions League.

(5) I falsely believe one of the statements (1), (2), (3) and (4).

This seems to me like a reasonable counterexample to Wittgenstein's doctrine.

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2Olle
topynate: It was only for reasons of space that I listed five events with probability 0.8 each, rather than 1000 events with probability 0.999 each; the modification is obvious. Eliezer: Point taken.
Eliezer Yudkowsky100

You need to work with probabilities, and then make statements about your expected Bayes-score instead of truth or falsity; then you'll be consistent. I have a post on this but I can't remember what it's called.

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1thomblake
I think Wittgenstein's point was that you're using 'believe' in a strange way. I have no idea what you meant by the above comment; you're effectively claiming to believe and not believe the same statement simultaneously. If you're using paraconsitent logic, you should really specify that before making a point, so the rest of us can more efficiently disregard it.