The Upshot | Could Donald Trump Drop Out? Some Bettors Seem to Think So

The 2016 Race

There’s a small but meaningful chance that Donald Trump will quit the race before Election Day, according to betting markets. Credit... Mark Makela for The New York TimesThe latest guessing game is whether Donald Trump will drop out of the presidential race before Election Day. Although his campaign has denied that this is a possibility, ABC News reports that senior Republican officials are taking the idea seriously enough that they are exploring how to replace him if he drops out.

So, what are the odds he quits?

One way to determine this is to look at the latest odds in political prediction markets. It’s not that any bettor knows what Mr. Trump will do. Rather, markets are useful because people putting their money where their mouth is are more likely to give an honest assessment than party insiders positioning for political advantage. Moreover, aggregating the intuitions of many traders usually beats relying on any group of pundits.

At the British prediction market Betfair, traders currently assess the Republican Party as holding a 25.8 percent chance to win the presidency. But they give Mr. Trump only a 24.1 percent chance of becoming president.

The difference of 1.7 percent probably reflects the possibility that Mr. Trump drops out and that an alternative Republican wins the White House.

That tells us the chance that Mr. Trump drops out and the Republicans still win. What about the odds that Mr. Trump drops out, and his replacement loses to Hillary Clinton? To determine those odds, some extrapolation is required.

As a starting point, let’s assume that Mr. Trump’s replacement is as likely to lose the election as Mr. Trump is. Note that the markets assess the chance that the Republicans lose — 74.2 percent — as being roughly three times greater than the chance of victory. As such, our assumption suggests that the chance that Mr. Trump’s replacement loses is also three times that of his chance of winning (which we already calculated to be 1.7 percent). It follows that the chance that someone other than Mr. Trump leads the Republican Party to a loss is then three times 1.7, or around 5 percent.

The odds that Mr. Trump drops out are simply the sum of the chance of an alternative Republican either winning (1.7 percent) or losing the election (5 percent), or 6.7 percent.

Perhaps instead, Mr. Trump will drop out only if or when the chances of a Republican winning have fallen sufficiently that continuing to campaign is not worth his time. If so, the previous calculation represents a lower bound on the odds Mr. Trump drops out. For instance, if Mr. Trump will drop out only when he has wrought sufficient damage on the Republican brand that his replacement has — to keep the math simple — a 17 percent chance to win the election, then similar calculations suggest that markets give Mr. Trump a 10 percent chance to drop out.

Perhaps the bias goes the other way, particularly if you believe — as I do — that the Republicans are more likely to win if Mr. Trump drops out. If so, my calculation represents an upper bound on the chance Mr. Trump quits. Perhaps an alternative Republican candidate has a 50 percent chance of winning, if given the chance. If so, then the chance that an alternative Republican runs and wins (which, if you recall, is 1.7 percent) is equal to the chance that an alternative runs and loses. By this view, the odds that Mr. Trump drops out are about 3.4 percent.

My own judgment is that it appears that the markets rate the chance that Mr. Trump drops out as being somewhere between 3 and 10 percent. The range of my estimate is wide partly because it is unclear precisely what assumption to use in extrapolating from market prices to the odds Mr. Trump drops out, and partly because these calculations are sensitive to small changes in betting odds.

How seriously should we take all of this?

The divergence between the odds of a Republican president and a Trump presidency is real. It is evident not only at Betfair, but also in the odds offered by an array of overseas internet bookmakers. No similar divergence appears between the odds of Mrs. Clinton assuming the presidency and the Democrats winning the election, suggesting that markets believe it’s a sure thing that she’ll be on the ballot.

Equally, it seems unlikely that these markets are privy to any sensitive inside information. Instead, they’re a useful aggregation of people’s best guesses. Some people call this the “conventional wisdom,” but I prefer to call it “collective wisdom,” to highlight that it is probably wiser than any of us individually. And that collective wisdom says that there’s a small though meaningful chance that Mr. Trump quits the race before Election Day.