Karen Tumulty at the Time blog Swampland perceptively writes:

“the easiest choice for endangered Democrats in swing districts is to vote against the bill–but only if it passes. That’s because they need two things to happen to get re-elected this fall. They need to win independent voters (who in most recent polls, such as this one by Ipsos/McClatchy, are deeply divided on the bill). But they also need the Democratic base in their districts to be energized enough to turn out in force–something that is far less likely to happen if Barack Obama’s signature domestic initiative goes down in flames.”

Tumulty compares the scenario to an earlier vote in 1993 on the Clinton economic plan:

“It was the night of August 5, 1993, and Bill Clinton was one vote short of what he needed to get his economic plan through the House–a vote he got, when freshman Marjorie Margolies-Mezvinsky switched hers. The other side of the Chamber seemed to explode. Republicans pulled out their hankies and started waving them at her, chanting: “Bye-bye, Margie.” Margolies-Mezvinsky learned the hard way that they were right. Her Main Line Philadelphia district was the most Republican-leaning of any represented by a Democrat in Congress. She had sealed her fate: During her campaign, she had promised not to raise taxes, and the budget proposed a hike in federal taxes, including a gasoline tax. On the day of the vote, she appeared on television and told her constituents that she was against the budget. Minutes before the vote, however, on August 5, 1993, President Clinton called to ask Margolies-Mezvinsky to support the measure. She told him that only if it was the deciding vote—in this case, the 218th yea—would she support the measure. “I wasn’t going to do it at 217. I wasn’t going to do it at 219. Only at 218, or I was voting against it,” she recalled.11 She also extracted a promise from Clinton that if she did have to vote for the budget package, that he would attend a conference in her district dedicated to reducing the budget deficit. He agreed (and later fulfilled the pledge). Nevertheless, Margolies-Mezvinsky told Clinton “I think I’m falling on a political sword on this one.”

Tumulty suggests the underlying game is the Prisoner’s Dilemma. Some of her commenters suggest the game is similar to the free-rider problem in provision of public goods. The free-rider problem is very similar to a Prisoner’s Dilemma so really the commenters are echoing her interpretation though they may not realize it.

I claim the interesting version of the game for Democratic Representatives in conservative districts is Chicken. Two cars race towards each other on a road. Each driver can swerve out of the way or drive straight. If one swerves while the other does not, the former loses and the latter wins. If neither swerves, there is a terrible crash. If both swerve, both lose. A variant on this game is immortalized in the James Dean movie “Rebel without a Cause”.

According to Tumulty, Democratic Representatives in conservative districts want to have their cake and eat it: they need healthcare reform to pass to get Democratic turnout but they want to vote against it to keep independents happy. The strategic incentives are easy to figure out in two scenarios. First, suppose the bill is going down however the Rep votes as it does not have enough votes. Then, this Rep should vote against it – at least they get the independents in their district. Second, suppose the bill is going to pass however the Rep votes – they should vote against via the Tumulty logic.

The third scenario is ambiguous. Suppose a Rep’s vote is pivotal so the reform passes if and only if she votes for it. At the present count with retiring Reps, Pelosi needs 216 votes to pass the Senate bill in the House so a Rep is pivotal if there are 215 votes and her vote is the only way the bill will pass. Margie M-M was in this position in 1993. There are two possibilities in the third scenario. In the first, the Rep wants to vote against the bill even when she is pivotal as she is focused on the independent vote. This means she has a dominant strategy to vote against it the bill.

This case is strategically uninteresting and, as in the Margie case, it is implausible for all the undecideds to have a dominant strategy of this form. So let’s turn to the second possibility – many undecideds Rep wants to vote for the bill if they are pivotal. This generates Chicken. If none of the conservative Democratic Reps vote for it, the bill goes down and its a disaster as Democratic voters do not turn out. This is like cars crashing into each other in Chicken. Your ideal though is if someone else votes for it (i.e swerves) in the pivotal scenario and you can sit on the sidelines and vote against it (drive straight). There is a “free-rider” problem in this game as in the Prisoner’s Dilemma. But there is a coördination element too – if you are the pivotal voter you do want to vote for the bill.

Chicken has asymmetric equilibria where one player always swerves and the other drives straight. This corresponds to the case where the conservative Democrats know which of them will fall on their swords and vote for the bill and the rest of them can then vote against it. This is the best equilibrium for Obama as the Senate Bill definitely passes the House. But there is a symmetric equilibrium where each conservative Rep’s strategy is uncertain. They might vote for it, they might not. There is no implicit or explicit coördination among the voters in this equilibrium. This equilibrium is bad for Obama. Sometimes lots of people vote for the bill and it passes with excess votes. But sometimes it fails.

There is lots of strategy involved in trying to influence which equilibrium is played. And there’s lots of strategy among the Reps themselves to generate coordination. If you can commit not to vote for the bill, Obama and Pelosi are not going to twist your arm and they’ll focus on the lower-hanging fruit. Commitment is hard. You can make speeches in your district saying you’ll never vote for the bill. Margie M-M did this but a call from the President persuaded her to flip anyway. Republicans are going to emphasize the size of the independent vote to convince the undecideds that they have a dominant strategy to vote against the bill. And the President is going to hint he’s not going to help you in your re-election campaign if you vote against the bill. Etc., etc.

So, if the Senate bill is finally voted on, as we creep up to 200 votes or so, we’ll see Chicken played in the House. We’ll see who lays an egg.