One approach is to reduce discontinuities and spoiler-effects in voting, which in turn reduces the incentives for a politician to accept—or someone else to offer—a devil's bargain. As it stands now, there's lots of potential for: "Do me a favor and my money will push you the small distance that distinguishes total defeat from total victory."

That leads to some game theory and math, with things like some form of ranked-voting, uncapping the House of Representatives, and maybe even proportional-representation rather than lots of just-one-winner races.