How much influence can news providers exert on the political process? 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. While existing media concentration measures are built by aggregating market shares across platforms, the new measure performs cross-platform aggregation at the level of individual voters on the basis of their attention shares. The paper derives a robust upper bound to media power over a range of assumptions on the beliefs and attention patterns of voters. Computing the value of the index for all major news sources in the United States from 2000 to 2012 results in four findings. 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 calibrated version of the model indicates that media power is much lower than the upper bound but still substantial
