Does media choice cause polarization, or merely reflect it? We investigate a critical aspect of this puzzle: How partisan media contribute to attitude polarization among different groups of media consumers. We implement a new experimental design, called the Preference-Incorporating Choice and Assignment (PICA) design, that incorporates both free choice and forced exposure. We estimate jointly the degree of polarization caused by selective exposure and the persuasive effect of partisan media. Our design also enables us to conduct sensitivity analyses accounting for discrepancies between stated preferences and actual choice, a potential source of bias ignored in previous studies using similar designs. We find that partisan media can polarize both its regular consumers and inadvertent audiences who would otherwise not consume it, but ideologically opposing media potentially also can ameliorate the existing polarization between consumers. Taken together, these results deepen our understanding of when and how media polarize individuals.