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Political commentators warn that the fragmentation of the modern media landscape induces voters to withdraw into 'information cocoons' and segregate along ideological lines. We show that the option to abstain breaks ideological segregation and generates 'cross-over' in news consumption: voters with considerable leanings towards a candidate demand information that is less biased towards that candidate than voters who are more centrist. This 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 centrist or only moderately biased. It also implies that polarisation of the electorate may lead to an ideological moderation in news consumption
