It’s certainly true as Kevin Drum says that one thing that happens when politicians don’t have the money to buy tons of television ads is that the guys who own newspapers get a lot of power. But I think it’s worth pointing out that this is just one of the many ways that money is bound to talk in the political system no matter what you do with campaign finance. Politicians are very dependent on lobbyists and trade associations not just for money, but for knowledge, expertise, and analytical capacity. But of course lobbyists and trade associations have those things in part because they cost money.
This is, I think, a pretty huge problem. But it’s not really one that can be solved by reducing people’s ability to give money to politicians. What’s needed are institutional reforms that give politicians more capacity to do analysis, and that put more political authority in the hands of politicians who have analytic capacity at their disposal. Whenever a decision is made “by the states” that means, in many places, that the decision is being made by term-limited part-time state legislators who have no practical alternative but to rely on lobbyists for guidance and information.