This paper defines the power of a media organization as its ability to induce voters to make electoral decisions they would not make if reporting were unbiased. It proposes a measure of power with two features. First, while existing concentration indices are built by aggregating market shares across platforms, the new measure performs cross-platform aggregation at the voter level. Second, rather than relying on a particular model of media influence, the paper derives a robust upper bound to media power over a range of assumptions on the beliefs and attention patterns of voters. Index values can be computed for the US in 2012 and reveal the following patterns. First, it cannot be excluded that the three largest media conglomerates could individually swing the outcome of most presidential elections. Second, in all specifications the most powerful media organizations are broadcasters: the press and new media are always below. Third, relative media power is well approximated by a simple function of attention shares. Fourth, a calibration exercise shows how empirical estimates of media ináuence can be used to refine the power index.