Rudy or the Minimax:
Game Theory, Giuliani, and the GOP Nomination

Politics — By Joe Carter on October 2, 2007 at 12:24 am

At a meeting of the Council for National Policy, several leaders of the “religious right” threatened to abandon the GOP in favor of a third party if Rudy Giuliani is the nominee. While I am closely associated with many of these groups I was dismayed by the news and considered it a tactical mistake. I’m in agreement with James Dobson who, according to the Washington Post, “spoke out against the idea of a third party even if ‘both Democratic and Republican nominees are known to be entirely unsupportive of the sanctity of human life, the institution of marriage and other aspects of the pro-moral agenda.’”
My fellow Christian conservatives are being a bit hasty for the the assumption that Giuliani will be the nominee is premature at best. I’m fairly confident that Republicans will come to their senses in time to choose a candidate that will not destroy the party. Eventually primary voters will realize that the reason the liberals in New York City elected the pro-choice, anti-gun, cross-dressing philanderer is because he was one of them — not one of us.
But while I’m cautiously optimistic that Rudy will flame out, I am distressed by the overreaction to this news item. Some of my fellow Republican bloggers–many of whom are even conservatives–leaped to the absurdly illogical claim that if social conservatives didn’t support Rudy, we’d be responsible for Hillary being elected.
Think about that one for a second.
Social conservatives do not want Hillary to be President, which is why they will not vote for her in the Democratic primaries. Social conservatives also do not want Rudy to be President, which is why we will not vote for him in Republican primaries. If these two candidates are on the ballot it will not be because of any positive steps taken on the part of social conservatives. Yet, according to the logic of my fellow Republicans, by not voting for a man who we don’t want to be President we are ensuring the election of a woman that we do not want to be President.
I assume that these bloggers know how the primary process works in America. If so they should be aware of the chain of responsibility. Primary voters who choose Hillary as the Democratic candidate are the primary group responsible if she gets elected. Without them there isn’t even the possibility that she can become President. Likewise, assuming that she can win the Electoral College, those who vote for her in the general election will be the ones who deserve the blame (or credit).
Unless social conservatives vote for Hillary in either the primaries or the general election, we are in no way to blame for her moving back into the White House. That blame will go to our friends and neighbors. The same goes for the nomination of Rudy.
But what if the reason that Hillary wins is, as some want to claim, because social conservatives did not choose the lesser of two evils and vote for Rudy? Again, we social conservatives are not to blame at all. We are the ones who will have made the rational choice during the primaries while the Giuliani supporters made an irrational choice.
To illustrate what I mean, let’s use the tools of game theory.


Imagine that you have three groups of voters. Group A likes Hillary and opposes all Republican nominees; Group B prefers Giuliani, but would choose another nominee over Hillary; Group C prefers anyone other than Giuliani and Hillary. The choices could be put on matrix like this:

 Hillary (1) Giuliani (2) Anyone Else (3)
 Hillary (A)       3        0           0
 Giuliani (B)      -1        3           2
 Anyone Else (C)      -1        0           3

Group A would be happy with A1, and unhappy with either A2 or A3. Similarly, Group B would be unhappiest with B1, happy with B2, and satisfied with B3. Group C would be unhappy with C1, dissatisfied with C2, and happy with C3.
Now let’s examine what rational choices each group of voters should make in a Republican primary.
Since the GOP is never going to nominate Hillary, the most rational choice for Group A would be to skip the Republican primary altogether and vote in the Democratic primaries. The most rational choice for Group C would be C3–anyone other than Giuliani. So what should Group B choose? Even though their first preference is B2, they have to consider how Group C will vote.
For Group B, choice B3 is what game theorists call the minimax condition, the choice which minimizes the maximum possible loss. They don’t get Giuliani but they don’t get Hillary either. (That same outcome, by the way, is the optimum choice for Group C.)
Even if they were unable to communicate with Group C, the most rational choice for Group B would be to choose the minimax. But they have even more incentive because social conservatives (Group C) have communicated to Giuliani supporters (Group B) that they will not accept option C2. All things being equal, it would therefore be irrational for primary voters to choose Giuliani.
But embedded in the calculus is the additional concept of “electability.” The assumption is that Rudy is more electable than any of the other candidates currently running for the Republican nomination. (Evidence for this claim is sorely lacking. In fact, I contend that Giuliani could not beat Hillary for a Senate seat, much less have a shot at besting her in a national contest.)
There are two assumptions buried in this idea of “electability.” The first is that he is electable because we social conservative will support him despite the fact that many of his positions and values are antithetical to our own. We will vote for him, they believe, because the alternative is even worse.
The second, related assumption is that Rudy is more palatable to the so-called independent swing voters than other candidates. They are also saying that the preferences of these independent voters are worth more consideration than those of social conservatives. We longtime Republican supporters are expected to set aside our moral qualms about the candidate simply because he appeals to a fickle group of swingers who may be able to affect the election.
In essence, we are being told to toss aside our principles and kowtow to the demands of a group of Republicans who have sold out conservative values for a pottage of pragmatism.
If that is what the GOP has become, then count me out. If Rudy is the nominee, then I and many other social conservatives will be staying home on Election Day. I’m telling you this now so that you can factor in this information when you are in the voting booth during the primaries. The time to choose the lesser of two evils comes during the primaries, not in the general election. If you think you can elect the Mayor without our help, then go with your first choice. But if you gamble and fail, you will be to blame. We offered you the minimax — and you chose Hillary.

    107 Comments

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