Binary decision theory predicts that voters prefer information sources whose biases conform to their own. We argue that voting is not a binary decision problem and that introducing abstention generates "cross-over" in news consumption (i.e., conservative voters consulting liberal media- and vice versa). Speci…cally, the option to abstain induces voters with considerable leanings towards a particular candidate to demand information that is less biased towards that candidate than voters who are less leaning towards that candidate. Moreover, non-monotonicity in the demand for slant makes voters' ideologies non-recoverable from their choice of news media and generates disproportionate demand for media outlets that are either centrist or only moderately biased.