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What game theory tells us about Wednesday's debate and the Republican primary

- September 18, 2015

Some of the candidates at Wednesday night’s Republican debate. (AP Photo/Mark J. Terrill)
Like Wednesday night’s debate, the race for the Republican Party’s presidential nomination is a free-for-all.
Although it is a crowded field, we can still make sense of the debate — and the longer battle for the nomination — with some canonical ideas drawn from game theory.
Lots of Republican voters are strategic
“Strategic” means that these voters are not necessarily voting for their true first choice.  That is, they are not voting “sincerely.”  Strategic voters are picking the candidate they like the most from the candidates who can actually win.
There was plenty of strategic voting in the 2012 Republican primary, as John Sides has noted. Many Republican voters chose Romney — largely because they believed he had the best chance in the general election — even though they were ideologically closer to another candidate.
It’s a winner-take-all race, which should narrow the field to two
In winner-take-all elections, the only “real” race is between the candidate who is leading and the candidate who is in second place.  While it is possible for (say) the third place candidate to rally and win, it is unlikely. This is true even in the primaries, where elections are spread over months.
Strategic voters who want to defeat the front-runner have to coordinate on an alternative
Donald Trump’s challenge is that being an early front-runner invites your opponents’ supporters to coordinate against you. Trump’s advantage — or any front-runner’s advantage — is that it may be hard for voters to coordinate on an alternative.
You can see that in the GOP race. There isn’t a clear second-place candidate. It was Jeb Bush for a while. Now it’s Ben Carson. And Wednesday’s debate may change that.
One possible way to achieve coordination is via focal points, a notion from Nobel laureate Thomas Schelling. A focal point in this context is a non-leading candidate that people realize that others will realize is a good candidate to start supporting.
You may have to read that sentence again for it to make sense: a focal point helps a group of people coordinate if every group member believes that the others will agree on that focal point.
So any candidate who wants to knock off the front-runner needs to stand out as the “focal candidate.”
Here’s what this means for strategy in a debate like Wednesday’s
Of course, merely speaking in a debate helps make a candidate stand out and potentially become the focal point.  But Wednesday’s debate added a twist: A candidate got to speak if another candidate mentioned him or her. Thus, by mentioning another candidate, you’re helping make that candidate a temporary focal point.
So if I were advising one of the candidates, here’s what I’d tell them.

  • First place candidate: Name the last place candidate by name. By all means, do not refer to the second place candidate.

Indeed, that’s the first thing Trump did by picking on Rand Paul — although, of course, it was difficult to sustain that strategy because the moderators were explicitly asking Trump to comment on many other candidates.

  • Second place candidate: Name the first place candidate by name. By all means, do not refer to the 3rd place candidate.

This means Carson should have focused more on Trump than on, say, Bush. The moderators helped him do that by asking him to address Trump several times.

  • Other candidates: Spend as much time as possible making yourself stand out from the other trailing (non-first or second place) candidates and mimic the things people find appealing about the first and second place candidates.

An example of this in Wednesday night’s debate was Carly Fiorina’s response about drug use. Fiorina took a fairly safe stance (drugs are bad, drug policy needs reform), but she took the stance in both a memorable and personal fashion and this stance clearly distanced herself from Bush.
Why the debate matters
In the end, Wednesday’s debate — just as the one in August — is a moment when everybody who is watching knows that everybody else who is watching is, um, watching.  Thus, the debate had its biggest impact by changing how people think other people view the candidates.
Consider the ascent of Carson to second place in the polls immediately following the August debate. Carson was focal after this debate for a number of reasons, but the more important aspect of the winner-take-all dynamic at play here were the strong performance of Trump and weak performance of Bush. After the first debate, the GOP simultaneously faced the reality that Trump was going to remain the front-runner, and Bush was much less likely to quickly vanquish him.
This focal point dynamic is a big deal when you think about it, with both negative and positive effects for democracy. On the one hand, this means that policy statements during a debate — most of which might not generate visceral reaction — will not tend to affect the candidates’ support.  Miscues, gaffes, and zingers will have sway beyond what one might naively hope for.
On the other hand, these “circuses” — even though sometimes light on policy content — might help the voters coordinate their beliefs about the candidates.  In so doing, even if the gaffes and zingers are superficial, the debates arguably provide structure to voters’ understanding of, if not what the election “about,” at least who the election is between.
John W. Patty is a political science professor at the University of Chicago.