Evan Soltas
May 10, 2015

Who's The Best Candidate?

Martin O'Malley: If drafted, I will run; but if nominated, I will probably be a disaster.

Without a doubt, one of the best parts of political elections are active prediction markets. For observers of prediction-market activity, a lot can be learned about how politics works.

I'm curious whether prediction markets can answer an important political question in the U.S.: Is someone a good candidate for president? And they actually can.

Prediction markets give us probabilities that candidates will win the Republican and Democratic nominations for president and the probability that they will win the general election. If we assume that candidates compete for only one nomination and cannot stage a third-party run if they do not win -- that is, no John Andersons allowed -- then we can easily estimate the probability of them winning the general election, conditional on winning the party nomination.*

When political pundits discuss whether someone is a good candidate for president, I think this conditional probability is exactly what they mean.

Taking these two probabilities from three different prediction markets -- PredictWise, Betfair, and PredictIt -- I am able to estimate this "competitiveness" score for nine top contenders for the Republican and Democratic nominations: Jeb Bush, Marco Rubio, Scott Walker, Rand Paul, and Chris Christie for the Republicans, and Hillary Clinton, Elizabeth Warren, Joe Biden, and Martin O'Malley for the Democrats. (Some technical notes can be found below.)

Here's what I find: The best Republican candidate is Jeb Bush, who has a 67-percent chance of winning the general election if he wins the nomination. The worst Republican candidate is Scott Walker, who has a 44-percent chance.

Among Democrats, Joe Biden and Hillary Clinton are nearly tied for the top candidate, with 58-percent and 57-percent chances of general-election victory if either secures the nomination. With a 24-percent chance, Martin O'Malley is the worst Democratic candidate.

You can see the full table of results here:

It's worth noting here that, at the party level, prediction markets estimate a 58-percent chance of a Democrat winning the presidency and a 42-percent chance of a Republican win. So comparing the candidate's conditional probability with the party's overall probability gives you a sense of good, say, Jeb Bush is as a candidate relative to the Republican field.

I found the results pretty surprising. They suggest that Rand Paul is a viable general-election candidate, Elizabeth Warren and Scott Walker are pretty overrated, and that "Bush fatigue" is fake. I was also surprised, in general, how closely clustered the top candidates were -- one take-away from this is that the candidate matters less than you might think.

On the other hand, the prediction markets think that the rest of the field is remarkably weak. Another take-away to the parties, then, might be: Nominate one of these candidates, or you will get crushed. This also helps explain why many of the top candidates can have better than 50-50 odds of winning in the general election if they win their party's nomination.

What might differentiate, say, Jeb Bush from Scott Walker in this conditional probability? I'll mostly leave that to the pundits. Yet Andy Hall, a young political scientist at Harvard, has recently found compelling evidence that political extremism hurts candidates' chances in general elections.

Another possibility is that these conditional probabilities aren't a perfect measure of competitiveness. If some of these candidates win the nomination, you've got to imagine that they got lucky -- Biden, for instance, trails Clinton in his chance of winning the Democratic nomination -- and so there's a sense in which this conditional probability is premised on "something good" happening to the candidate.

I would also remind readers about the "no-John-Andersons" assumption. If a candidate could stage a viable third-party race -- one might imagine this for Warren or Paul -- then my estimates might be a bit low.

Assessing the viability of presidential candidates is too important to be left to polling and pundits. Prediction markets can shed some light on whether a candidate has a shot in the general election if they win their party's nomination. 



* I will step through the math. By the law of total probability:

P(wins election) = P(wins election | wins nomination)*P(wins nomination)
                                        + P(wins election | ! wins nomination)*P(! wins nomination),

and then by assumption that P(wins election | ! wins nomination) = 0 :

P(wins election) = P(wins election | wins nomination)*P(wins nomination)

and therefore

P(wins election | wins nomination) = P(wins election) / P(wins nomination).

** Two technical notes:

(1) Since prediction markets for both the nomination and the general election do not exist for all candidates, I wasn't able to go further than the top names. Another issue, for some long shots, was that the probabilities are coarsely estimated -- that is, if you have about 2-percent chance of winning the nomination, whether that 2-percent is really 2.4 percent or 1.6 percent matters, and I do not have that level of precision. So I excluded candidates that prediction markets see as long shots. 

(2) Prediction markets are Dutch-booked to ensure profits for the market maker. To correct for this, I re-based the relevant probabilities so that they summed to one.