We present a novel explanation for the group polarization effect whereby discussion among like-minded individuals induces shifts toward the extreme. Our theory distinguishes between a quantitative policy under debate and the discussion’s rhetorical frame, such as the likelihood of an outcome. If policy and frame position are mathematically related so that frame position increases more slowly as the policy becomes more extreme, majority formation at the extreme is favored, thereby shifting consensus formation toward the extreme. Additionally, use of a heuristic frame can shift the frame reference point away from the policy reference, yielding differential polarization on opposing policy sides. We present a mathematical model that predicts consensus policy given group member initial preferences and network structure. Our online group discussion experiment manipulated policy side, disagreement level, and network structure. The results, which challenge existing polarization theory, are in qualitative and quantitative accord with our theory and model.