[madnak]

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if we know someone has used an illogical method to arrive at an answer to a yes/no question, and that is ALL that we know, then, given the information we have, they are 50% to be correct. (assume we do not know the question, we do not know the answer, and we do not know who the person shares/doesn't share a viewpoint with etc)

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I don't think this is true. This seems similar to saying 1/infinity=0. It seems to make sense, in most cases it works, but it's not actually true. I don't think we can talk about probability in a vacuum. Take proposition n - a yes/no proposition. You know nothing, nothing at all. Is proposition n 50% likely to be true given your knowledge?

I think we can say that of all boolean propositions that have a value (we'll ignore the proposition "this statement is false"), there are as many true propositions as false propositions. I don't know that this necessarily implies that a random proposition has a 50% chance of being true. I think this is one of those tricky places where infinity destroys normal methods of assigning probability.

Is a random number 50% likely to be positive and 50% likely to be negative? In general we can assume so without running into problems, but I'm not convinced that the answer is "yes." Excluding 0 just to make things easier, there are just as many numbers on the negative side of the number line as on the positive side. This means a number is 50% likely to be negative and 50% likely to be positive, right? But wait - there are as many numbers below -(10^500) as above -(10^500). In fact, for any given number at all on the number line, there are as many numbers to the left of that number as to the right of that number. And we can say it doesn't matter, because even an arbitrarily large number is finite rather than infinite, and is overwhelmed by the infinity of the number line, but then we're basically saying that finite/infinite=0.

I do think I understand the point you're getting at, and trying to explain to Lestat. I've been thinking about how to describe this point since David's post about extrapolating intelligence trends. But I haven't figured it out. I said then that a stupid person have an edge over a smart person unless a random outcome would also have the same edge. That wasn't true, and was a bad way to express it. I think in this case I want to say something like "an illogical person will never be worse than random on average," but that's not quite what I want to say either. What do I want to say? I'll keep thinking about it.

For the specific purposes of this discussion, I do believe that a hypothetical illogical person is no worse than a coin-flip. In fact, an illogical person may be the same as a coin-flip. Unfortunately, I can't figure out how to demonstrate this principle (much less generalize it).