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Getting ahead early might cost you your head: a bit of game theory about primary campaigns

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Thinking about multicandidate elections is tricky (as I have written about here and here). Let's work this out a bit, and see how it speaks to the Republican nomination contest.

A lot of simple narratives revolve around "standing out from the field." By making oneself seem like the best (or at least the most popular) candidate, the logic goes, voters will recognize either appeal or inevitability and flock to your camp.

This logic is not silly. But it avoids the fact that campaigns consist of more than two steps. The "standing out" logic is reasonable if one conceives of an election as "Step One: Candidates stand up. Step Two: Voters look at the candidates and then vote." That's a minimal conception of a campaign, and too slim a fit to capture the girth of the GOP presidential struggle.

In US presidential primary campaigns, there are a lot of "step ones." That is: Candidates stand up, candidates and voters all look around, then candidates try to smack and/or protect each other, after which some of the voters vote, after which some of the candidates sit down, leaving the remaining candidates to smack and/or protect each other, after which a different set of the voters vote, after which…

You get the point.

We don't need all of the various rounds (there are 19 for the GOP primary); considering only two rounds will suffice to make the basic point. Suppose that 1) the person who stands highest at the end gets all the votes, 2) every candidate wants to get all of the votes, and 3) each candidate can "smack down" any other candidate in the second round.

I'll leave some details to the side here, because this is a blog post, not a scholarly article. The basic intuition is this: Any candidate who stands up in the first round is at greater risk of being smacked down in the second round. The details I omit play an important role in determining who will stand up, but the simple fact is that multiple rounds of an election — with campaigning and attacking — quickly lead to a "tortoise and hare" result. Namely, the early leader is not necessarily the one who is most likely to win.

This thought experiment demonstrates that such a conclusion is not necessarily due to "voter fatigue" or some other public opinion phenomenon — it could be due to the strategic calculus of office-seeking candidates.

In the struggle for the GOP nomination, there are many (though dwindling) candidates pursuing the votes. The two first contests in Iowa and New Hampshire are understandably being (over)analyzed for the tea leaves they may contain about the future of the struggle and, ultimately, who will be elected president in November. But the simple thought experiment described above suggests that, thinking through the strategic dynamics of the process, it's very hard to believe anything like "momentum" should describe primary campaigns.

Some candidates win early because there are no other viable challengers. But when there are, it's not at all clear that the early bird will get the votes: He or she might indeed just get the worm. If you doubt this, simply ask Howard Dean … or (for now at least) Jeb!