The game theory of Lieberman punishment

Democrats are upset at Joe Lieberman's defection from the proposed health care reform compromise in the Senate, but don't know what to do about it. Annoying Lieberman by denying him time to speak on the floor may make Al Franken feel better, but it also raises the odds of a damaging party switch. (Despite his propensity to annoy the base on high-profile issues, Lieberman's voting record through July actually places him near the center of the Democratic party caucus.) The same problem applies even more strongly to proposals to strip him of his seniority or his chairmanship of the Homeland Security committee.

I'm not sure it's worth the risk -- party switchers tend to drastically change their voting patterns -- but a better punishment strategy was suggested by Sandeep Baliga of Northwestern's Kellogg School back in November. Drawing on game theory, he suggests creating a "penal code" in which Democrats "[forgive] Lieberman gradually over time to get his cooperation in the future":

Independent Joe Lieberman is driving Gail Collins and the progressive left crazy. He caucuses with the Democrats and holds a plum committee chairmanship on the strength of largely voting with the Democrats. But he is threatening to filibuster the healthcare reform vote in the Senate. The only way to give him the incentive to drop this threat is to threaten him in turn – strip him of his chairmanship if he filibusters the vote.

The problem is that Lieberman knows that if he filibusters, the Democrats do not have the incentive to carry out their threat because they need his vote in the future. Their threat to strip him of his chairmanship is not credible. This is a classic issue in deterrence theory: how can we make our threat to bomb the Soviets if they bomb us credible? Many of the strategies do not transfer... but one does: the Democratic leadership has to rely on reputational devices to incentivize Lieberman.

Forgiving Lieberman may create future defections as the Democratic leadership shows they are wimps. Carrying out the threat shows that Reid and Obama are tough and signals they will be tough in the future. This is the slippery slope argument and the classic “act crazy to get a reputation for toughness” strategy...

If Lieberman finds the threat credible, the Democrats do not even have to carry it out because he will not filibuster. But if he does not find it credible, he will filibuster. Then you face the problem of losing his vote in the future if you accept the slippery slope argument and feel you must punish Lieberman for his treachery.

To evaluate this possibility, we have to consider the credibility of Lieberman’s threat to vote Republican in the future if he stripped of his chairmanship. The Republicans are too extreme for the Connecticut voter. If Lieberman votes with them or switches parties, he is in trouble at home. So you can rely on his reelection motive to discipline him and get his vote on some mainstream Democratic issues.

There is also a subtle way to give Lieberman the incentive to go along with his punishment without ganging up with the Republicans. It is a “penal code” to design dynamic incentives and it was discovered by Dilip Abreu. The penal code boils down to forgiving Lieberman gradually over time to get his cooperation in the future. In this scenario, this requires some deviation from standard seniority principles for allocation of committee chairs. Put a stopgap person, Al Franken, in charge of Lieberman’s committee. Tell Lieberman that Franken will step down if Lieberman is on board in future. Otherwise, goodbye chairmanship forever. If this subgame is triggered as Lieberman is bloody minded, Franken should step down in favor of whoever is in line for the chairmanship now if Lieberman is ejected. This might be necessary to get this person on board with the plan to deviate from the status quo procedure for allocation of committee chairs.

In reality, the requirement to deviate from seniority makes any such proposal difficult to implement. Regardless, however, Baliga's post is useful in illustrating the subtlety of the incentive problems faced by Harry Reid and the Democratic leadership.

Comments

[David]

It's perhaps noteworthy that Prof. Baliga only dealt with one side of the problem. The Republicans are also trying to get Lieberman to vote their way. The omission may show that Prof. Baliga, like most academics, identifies with the Democrats.