I think it would be better to use the marketplace than regulation. They are licensed so there could be criterion built into the licensing both to present both sides and to have fact checking with fines for lies/slander.
Monopoly is not a marketplace.
I have given this concept much thought, and I used to believe that we should allow "the market" to solve all problems, but even Adam Smith warned us about the creation of monopolies.
"The Market" can't solve this problem anymore than the market could solve the problem of John D Rockefeller and Standard Oil. Like the media, Standard Oil was so big it could control the market.
They are licensed so there could be criterion built into the licensing both to present both sides and to have fact checking with fines for lies/slander.
This isn't just a matter of allowing both sides to have access. The media is biased left all the way down to the cameramen and janitors. New York voted for Barack Obama by an 88% margin. The employees of the media companies are hired from that pool of people and they cannot help but be biased.
I think the only way to insure fairness is by insuring half the employees are conservatives, because bias can slip in simply as a consequence of people's world view. They can't even help it. The only way to prevent it is you have to have people with a different World View and different biases. With this method, both sides can keep each other honest.