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For starters, fallacy means a flawed truth. Fallacy of composition means a flawed assumption of truth.
I read heard it this way...

Think crowded baseball game. You can't see because of the guy in front of you. If you stand up, then you can see. However, the fallacy of composition is that if EVERYBODY stands up, nobody can see the game any clearer than if they were all sitting down.
by Forest for the trees December 25, 2009
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