When people talk about US politics, they often focus on the various candidates’ “electability”. In particular, they talk about basing their support for a given candidate in the primary on how likely that candidate is to win the election.

This is a perfectly reasonable thing to think about, of course. If your primary goal is, say, to get a Democrat into the White House, then it makes sense to pick the Democrat who’s most likely to get there, even if that’s not your favorite candidate. The only problem is that, I suspect, people are often quite bad at guessing who’s the most electable candidate.

Eight years ago, I observed (1,2,3) that there is one source of data that might help with this, namely the political futures markets. These are sites where bettors can place bets on the outcomes of the elections. The odds available on the market at any given time show the probabilities that the bettors are willing to assign to the various outcomes. For instance, as of yesterday, at the PredictIt market, you could place a bet of $88 that would pay off $100 if Hillary Clinton wins the Democratic nomination. This means that the market “thinks” Clinton has an 88% chance of getting the nomination.

To assess a candidate’s electability, you want the *conditional probability* that the candidate wins the election, *if* he or she wins the nomination. The futures markets don’t tell you those probabilities directly, but you can get them from the information they do give.

Here’s a fundamental law of probability:

P(X becomes President) = P(X is nominated) * P(X becomes President, given that X is nominated).

The last term, the conditional probability, is the candidate’s “electability”. PredictIt lets you bet on whether a candidate will win the nomination, and on whether a candidate will win the general election. The odds for those bets tell you the other two probabilities in that equation, so you can get the electability simply by dividing one by the other.

So, as of Saturday, December 5, here’s what the PredictIt investors think about the various candidates:

Party | Candidate | Nomination Probability | Election Probability | Electability |
---|---|---|---|---|

Democrat | Clinton | 88.5 | 57.5 | 65 |

Democrat | Sanders | 12.5 | 6.5 | 52 |

Republican | Bush | 9.5 | 4.5 | 47 |

Republican | Cruz | 25.5 | 10.5 | 41 |

Republican | Rubio | 39.5 | 19.5 | 49 |

Republican | Trump | 25.5 | 15.5 | 61 |

(In case you’re wondering, the 0.5’s are because PredictIt has a 1% difference between the buy and sell prices on all these contracts. I went with the average of the two. They include other candidates, with lower probabilities, but I didn’t include them in this table.)

I’ve heard lots of people on the left say that they hope Donald Trump wins the nomination, because he’s unelectable — that is, the Democrat would surely beat him in the general election. I don’t know if that’s true or not, but it’s sure not what this market is saying.

Of course, the market could be wrong. If you think it is, then you have a chance to make some money. In particular, if you do think that Trump is unelectable, you can go place a bet against him to win the general election.

To be more specific, suppose that you are confident the market has overestimated Trump’s electability. That means that they’re either overestimating his odds of winning the general election, or they’re underestimating his odds of getting the nomination. If you think you know which is wrong, then you can bet accordingly. If you’re not sure which of those two is wrong, you can place a pair of bets: one that he’ll lose the general election, and one that he’ll win the nomination. Choose the amounts to hedge your bet, so that you break even if he doesn’t get the nomination. This amounts to a direct bet on Trump’s electability. If you’re right that his electability is less than 61%, then this bet will be at favorable odds.

So to all my lefty friends who say they hope Trump wins the nomination, so that Clinton (or Sanders) will stroll into the White House, I say put your money where your mouth is.

Thanks for producing the table. The numbers are interesting. There are two points I think should be made about their interpretation, one of which is practical and the other theoretical.

The practical issue is that you can’t place an actual bet at the implied probabilities quoted, because of the bid/ask spread. For an actual bettor it would be more useful to list a range covering the general election bid divided by the primary ask up to the general election ask divided by the primary bid. If your subjective estimate of the implied probability is lower than the lower end of this range you should buy in the primary and sell in the general, and vice versa if your estimate is higher than the higher end of the range. If your estimate is within the range then you shouldn’t bet.

The theoretical issue is more interesting. Or at least it’s more interesting to me, but then again I’m a mathematician, so almost by definition I find theoretical issues more interesting than practical ones. It’s that conditional probabilities of winning the general election conditional on receiving the primary nomination don’t exactly reflect “electability” as I think most people understand that term. The conventional wisdom is that parties balance electability, where centrist policy positions are considered an asset, against ideological conformity, where centrist positions are more of a liability. To be concrete, Republican voters and donors might prefer the policy positions of Ted Cruz to those of George Bush, but might think the latter has a better chance of defeating whomever the Democrats nominate, so they would have some doubts about both, though they are different types of doubts. The conditional probability effectively describes a bet which is only placed only the relevant candidate has been nominated, which means if he has at least partially overcome those doubts. A conditional bet on Cruz is a bet that he will be elected in the general election assuming he manages to convince a large slice of the Republican electorate that he could be. A conditional bet on Bush is a bet that he can win the general election if he manages to convince many Republican voters that his views are closer to theirs than they currently believe, and therefore presumably farther from those of typical general election voters

I suspect that by the term “electability” most people mean the candidate’s chances of success in the general election assuming voters’ current perceptions of them remain unchanged, rather than their chances in a world where those views have changed enough for them to have won the primary. If this is correct, and the conventional wisdom about the tradeoffs of the nomination process applies, then we should expect two systematic biases. Conditional probabilities should overstate the electability of extremist candidates relative to centrist ones, since the former will have overcome doubts about their electability to get nominated while the latter may have to shift away from the political centre. Also, conditional probabilities should overstate the electability of underdogs in the primary contest. A world where Clinton is the Democratic nominee is a fairly familiar one. A world where O’Malley is the Democratic nominee is one where he is vastly more popular, and almost certainly a better politician, than he currently seems to be, and so has a much better chance in the general election. I wouldn’t expect this bias to apply to non-candidates, however. A world where Ryan is the Republican nominee, despite not being a primary candidate, is one where a messy primary season has led to a deadlocked convention ending in awkward compromise. That’s not a good position from which to launch general election campaign.

It’s great to hear from you, John!

You’re absolutely right about the first point. I’m glad you mentioned it. Another practical concern is the opportunity cost of placing the bet. (You should only place a bet if the expected return is greater than the expected from whatever other investment you would have made with that money during that time.)

I want to think a bit more about your other point.