That same skeptic’s eye would also tell our hypothetical undecided that neither side is being entirely honest about the costs of its approach. The Democrats are pretending that taxing the rich can pay for almost everything. The Republicans are pretending that neither today’s taxpayers nor today’s seniors need bear any of the burden. The high-information swing voters are basically left to decide which dishonesty is worse, and which unacknowledged cuts or tax hikes they’d rather risk having to bear.

Finally, the more our hypothetical voter knows about how Washington works, the more obvious it becomes that all of this will be hashed out over years of negotiated back-and-forth — because no legislation passed with a razor-thin majority can endure unchanged for decades, and any enduring settlement will have to leave both sides a little unsatisfied.

If you want to think well of swing voters, and imagine them as wise Athenians rather than a Colosseum-going mob, you could see the improving odds for what once seemed like an unlikely 2012 outcome — a Romney victory in which Democrats hold the Senate — as a nod to the necessity for bipartisanship, and an attempt to make a significant change in Washington while also forcing both parties back to the negotiating table.