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Sniffnoy comments on Willing gamblers, spherical cows, and AIs - Less Wrong
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It seems to me that this is potentially informative -- if you're not certain enough that you're right to be willing to take the bet, this is a signal that maybe you should rethink your probability estimates or position. (Really of course you'd want to update according to Bayes, of course, but that's hard in general.)
(Spelling nitpick -- you've repeatedly misspelled "lose" as "loose". Would you mind fixing that?)
It's not a sign that your initial probability estimate was off.
Suppose that... I dunno, elections and sports matches aren't great examples, I'm just going to use an arbitrary proposition p and it helps if you imagine p isn't the kind of thing people make dumb bets about out of enthusiasm for "their team." If you'd reject an even-odds bet for both p and ~p (even ignoring transaction costs and declining marginal utility and tossing in the extra penny and so on), plausibly that's because you should start off with a probability estimate of 0.5 or so but once you know which side of the bet the other guy wants to take, you should update to give the side of the bet the other guy wants a probability higher than 0.5.
That's the motivation for stipulating the bookie doesn't know anything more about the proposition they want to bet on on than you do.
Also, thanks for catching the spelling errors.
"loosing" is still incorrect.
Suggest making the link explicit with something like this: "in spite of the fact that they're apparently irrational enough to be part of that public in the first place."
Gah. Now it should be fixed.