The House vote on health care reform

Jonathan Bernstein on the House whip count:

To review: there are probably about fifty House Democrats who want the bill(s) to pass, but without their vote, and the Democratic leadership (I'm going to call them "Pelosi" but it's really the House leadership and the White House) need a lot of them to vote yes. Many of them have already said -- and most of the rest know, and a few of them fear -- that they will vote yes if they need to, but otherwise they're going to vote no. So what's actually happening is mostly a coordination problem, and much of it will be hard for outsiders to see...

What Pelosi is dealing with is a list of fifty or so people, each of whom she understands to be (whatever they say) with her if she needs them, and each of which is probably saying (in one way or another): don't make me do it. Put me at the bottom of your list. And she has to gauge who is bluffing and who isn't, who she wants to protect from the effects of a no vote and who she doesn't, who really ranks where on that list.

I'd like to see this modeled mathematically. It sounds like each of the wavering Democrats is making a time-inconsistent promise to vote "no" on the bill - time inconsistent because they want the bill to pass, so if they're the 216th vote, they'll vote "yes" regardless of their earlier promise. But there must be some probability that each waverer will actually vote "no" when push comes to shove, either because of a cost-benefit calculation or petulance. What is Pelosi's optimal strategy if she knows this probability? If she doesn't know this probability? If she knows/doesn't know each waverer's costs of voting "yes"? Is there a market mechanism that would elicit truthful commitments from enough waverers to pass the bill?