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Two or more Twitter users who engage in a text battle on the popular social media site, most notably celebrities. A comment, opinion or taunt provokes a pride-driven response and feelings are vented for all to see.
Some people are just easily provoked, that's why Chris Brown keeps finding himself in a Twitter feud with somebody.

Best Twitter feud, no question Aimee Mann and Ice-T.
by Soapy Johnson August 17, 2011