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No, because extremist propaganda does not "average out" to an objective center.

If you want to distribute it in a box labeled "extremist propaganda", to study it as such, sure.

But if your society has some extremist propaganda in the wild, distributing more, different extremist propaganda will make things strictly worse.

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Who defines what is extremist propaganda? The people who win the propaganda war and get to label the other side as extremists is the answer.
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Extremism can be more-or-less objectively defined in terms of difference from the mean/median. Measurement is tricky but just because something has fuzzy boundaries doesn't mean it's meaningless. Especially when something is not near that fuzzy boundary.
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