“My opponent is a no-good, rotten cheater out to destroy America…”

Well, the primary campaign season sure has been heating up. As expected, we see that the candidates are really going after each other, making outlandish remarks, the whole shebang. This isn’t anything new: even back in June, former Minnesota governor Tim Pawlenty accused former Massachusetts governor Mitt Romney of being complicit in the formulation of the Democrats’ controversial health care reform plan, calling it “Obamneycare.” Clearly, with the jam-packed field and a necessity to beat the other contenders to get to the main event, there is a strong incentive for the candidates to go after each other’s throats.

Yet there is a major tradeoff in doing so. All of these candidates would very much prefer, even if they personally do not win the Republican nomination, that one of the other Republicans beat Obama in the general election. But by attacking their competitors, they decrease the chance of that happening.

Let’s assume that a candidate’s chance of winning is proportional to the amount of flak that is not directed at him or her. Thus, if each candidate i (of N total) generates f_{i,j} flak towards candidate j, then each candidate’s share of the flak is \frac{\sum_{j=1}^{N}f_{j,i}}{\sum_{k=1}^{N}\sum_{j=1}^{N}f_{j,k}}

However, by being the victim of more flak, the chances of beating Obama get smaller and smaller: voters are much less likely to vote for a candidate who has a terrible reputation, as bestowed upon him or her by his or her opponents. We can therefore set up a threshold at which the voters will not vote for candidate i: once he or she has taken more collective beatings than threshold F^{*}, Obama automatically wins (we can model Obama’s chances of winning as increasing in the amount of trashing his opponent has received; the main idea of the result will remain the same). Scary thought if you are a Republican, no?

Each candidate gets payoff R for being the nominee, as well as an additional payoff P if he or she wins the general election. The other candidates get payoff 0 if they lose the nomination and the presidency, while they get payoff V if a different Republican candidate wins the general election. Assume that R>V – candidates would rather be the nominee themselves, and get a shot at the presidency, no matter what the other candidates’ chances are.

This being the case, despite the preference to beat Obama, Republican primary candidates can always do better by hacking at each other as much as possible. Think about it – given any fixed amount of flak the other candidates are giving you, your chances of being the nominee go to one as the amount you attack them goes to infinity. This strategy (given finite amount of flak from others) will yield a payoff of approximately R, which we stipulated was greater than V. Hence the Democrats will automatically win.

Note that this isn’t quite a Nash equilibrium, since the set of possible options is not bounded. Yet some of the normal game theory ideas are still visible here: what will end up happening, based on the incentives, is that the Democratic candidate gets re-elected. Nevertheless, the result depends on several assumptions: that the Republicans can attack each other to an arbitrarily large extent, and that they would always rather be the nominee than let someone else win. Still, it is interesting to observe that the situation as modeled here leads to an automatic Republican loss in November 2012. Pretty ironic, given that one would think that the entire purpose of the campaign is to unseat Obama.

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Hot deficit potato!

I had originally wanted to share some really cool veto math today, but I’m really fascinated by the chicken endgame being played out — it has to be periodic and not simultaneous near the end. Vetoes will have to wait.

Deficit chicken is starting to look a lot like hot potato in these final days before August 2nd. Even though bank analysts believe the Treasury will be able to hold things together for a few days longer, it’s probably in everyone (in the District)’s interest to take the deadline seriously — better the deadline you know than the one you don’t.

Even if default and/or downgrade don’t happen, Congress is quite aware that the situation is FUBAR and that passing the blame is the name of the game. Whichever of the Dems, GOP, or Obama happens to say the last “no” via veto, filibuster, or downvoting by the time the deadline rolls around will be blamed for preventing legislation of any kind from passing. Whereas we have previously modeled the situation as a game of Chicken, by now we can pretty much count the number of days it will take to get anything through the legislature. Now, if you’re unfamiliar with the game, Hot Potato involves passing an object back and forth or in a circle while music plays. The loser is the player holding the potato when the music stops.

In our game, all parties know exactly when the music will stop, and if all threats to defeat, filibuster, and veto are actually carried out, one of the three players is going to have to say the last “no.”

This is why I don’t find Obama’s threat to veto House Speaker Boehner’s bill (if it passes in both houses) credible — if he vetoes, legislature is basically out of time to draft something else that will pass in both houses. Obama would almost certainly get stuck with the hot potato.

No wonder he’s upset — it’s a Catch-22 for him, since he’s already looking weak to the Democrats for offering such a steep compromise. But, “singlehandedly” causing a default would be much much worse for Obama, which is exactly what the Tea Party hobbits seems to want, according to Senator McCain.

So, why is Obama making this threat in the first place, if it’s not credible? If he makes it seem like vetoing the bill is on the equilibrium path for him, it saves the Senate Democrats some face if they kill Boehner’s bill if/when it arrives in Senate. Otherwise, if the bill is stopped in the Senate, the Democrats in Senate will be left holding the hot debt potato at the end of the game.

Meanwhile, Senator Reid is biding his time before putting his version of a compromise to vote in the Senate. If Boehner’s bill fails to pass today, Reid will have the upper hand because he figures there’s just enough time left to pass his bill in both houses. Obama is supportive, so there’s no threat of veto, and even if the Senate Republicans filibuster as they’ve threatened to do, the GOP will certainly be saddled with the blame, since filing for cloture will set Senate back at least a day or two[1]. If it passes in Senate, the House has little choice but to pass the bill, or be blamed. Unless, of course, they really believe there’s more time to continue tossing the potato, or that doing this might actually make Obama look bad.

Quote of the day, from Reid: “Magic things can happen here in Congress in a very short period of time under the right circumstances.” Right circumstances => Not when filibustering is involved.

A very simplified game tree follows:

As we can see, all current threats, if carried out, lead to someone’s becoming a scapegoat. Interestingly, even though it looks like Boehner might get the votes he needs today, the Senate Democrats are using some excellent commitment strategy, by leaking a letter signed by all 53 members (hey, it looks like they didn’t get Joe Lieberman the Independent on the bandwagon) stating that they do not support the Boehner bill.

Next time: how having veto-power can hurt your outcome.

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[1] If the GOP decides to filibuster until the Fed defaults, it’s going to be pretty hard to pin this on Obama. Just saying.
[2] Fun infographic table thingy.