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Lumifer comments on Rationality Quotes November 2013 - Less Wrong
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Theoretically, if you treat your own previous position as a prior and the other guy's arguments as some evidence, the standard updating will lead you to have a new position somewhere in between which will look like a compromise.
Obviously there are are lot of caveats -- e.g. the assumption that an intermediate position makes sense (that is, the two positions are on some kind of continuous axis), etc.
Not to the extent your current position already takes those arguments into account (in which case the arguments fail to address any disagreement). More than that, by conservation of expected evidence some arguments should change your mind in the opposite direction from what they are intended to argue.