At the risk of wading in above my head here, I’m going to try to play out this thing a bit more. Thinking of the health care vote in game-theoretical terms is an interesting thought exercise, and while the lighthouse story is a good way of conceptualizing the predicament in the House in the simplest way possible, I would note some further wrinkles that make the situation a lot more complicated:
A quick note on how to classify the game: I don’t think it’s a Volunteer’s Dilemma because there’s a “sucker’s payoff” — cooperating when others defect is worse than everyone defecting. I’d say it is essentially a n-player Prisoner’s Dilemma (see also: Diner’s Dilemma), but with a few tweaks.
How do we rank the payoffs? As Karen said, the best payoff for many fence-straddling House Dems is to vote “no” and have the bill pass. For those same lawmakers, the sucker’s payoff would surely be a “yes” vote while the measure fails. In a classic Prisoner’s Dilemma, mutual cooperation is better than mutual defection, but I’m not sure that translates uniformly to this situation. Each congressman is different, and some may ultimately prefer voting against a bill that goes down to supporting legislation that makes it through.
Commenter mfbattle noted the lighthouse never got built in his experience, and defection is always the rational choice in a single game of Prisoner’s Dilemma. But this scenario is not an isolated one; serving in Congress is a series of “iterated” dilemmas. Past experience or future expectations may well affect the outcome.
To oversimplify a bit, two of the most successful strategies in an iterated Prisoner’s Dilemma are “tit-for-tat” and “win-stay, lose-switch” (also known as Pavlov.) Tit-for-tat takes cooperation as a baseline position and only defects in retaliation. If we consider last year’s vote on the House bill to be the last iteration, players using tit-for-tat would cooperate (vote “yes”) this time around. With Pavlov, a player simply uses what worked last time or switches if their strategy failed. In this case, the players in question using Pavlov would defect (vote “no”) because it worked out fine for them on the last vote.
Regardless, the n-player Prisoner’s Dilemma frequently results in something known as the Tragedy of the Commons. Individuals use up a commonly desirable resource (in this case, “no” votes) to the detriment of everybody involved (the bill doesn’t get passed.) But rather than being an inevitability, this is where political pressure and gamesmanship comes into play.
There is not “perfect information,” by which I mean the players don’t necessarily know what strategy others are pursuing or who has promised to do what. Players must depend on the word of other players or the leadership to determine if their cooperation is absolutely needed. All parties have an incentive to say they will defect (vote “no”) — it puts pressure on others to cooperate, increasing their own chances of getting the best payoff (voting “no” and having the bill pass.) At very least, players will not want to give away their position too soon (as evidenced by Reps. Adler, Altmire and Baird on the Sunday shows today.)
In reality, there are an incalculable number of lurking variables at play — promises from the president or Speaker Pelosi, new polling from their districts that changes perceptions of re-election prospects, the appeal of legacy votes for retiring Dems, etc. And that says nothing of the power of a moral argument; anti-abortion Democrats who believe the Senate language is insufficient or representatives that see the bill in terms of saving human life on a grand scale may not act in their own political self-interest.
Bottom line: There are (currently) 37 Democrats who voted “no” on the House bill, a handful of liberals unhappy with certain elements of the Senate bill, as well as Stupak’s anti-abortion bloc all trying to win concessions while contemplating the future of the Democratic Party and their own political needs in November.
If our little detour into game theory geekishness tells us anything, it’s that Pelosi and company have an immensely complex equation to solve and little time to do it. They’re just hoping one of these scenarios will add up to 216.