# Electability update

As I mentioned before, a fair amount of conversation about US presidential politics, especially at this time in the election cycle, is speculation about the “electability” of various candidates. If your views are aligned with one party or the other, so that you care more about which party wins than which individual wins, it’s natural to throw your support to the candidate you think is most electable. The problem is that you may not be very good at assessing electability.

I suggested that electability should be thought of as a conditional probability: given that candidate X secures his/her party’s nomination, how likely is the candidate to win the general election? The odds offered by the betting markets give assessments of the probabilities of nomination and of victory in the general election. By Bayes’s theorem, the ratio of the two is the electability.

Here’s an updated version of the table from my last post, giving the candidates’ probabilities:

PartyCandidateNomination ProbabilityElection ProbabilityElectability
DemocratClinton70.54463
DemocratSanders28.519.568
RepublicanBush8.53.541
RepublicanCruz13.55.40
RepublicanRubio32.51546
RepublicanTrump47.5
29.562

As before, these are numbers from PredictIt, which is a betting market where you can go wager real money.

If you use numbers from PredictWise, they look quite different:

PartyCandidateNomination ProbabilityElection ProbabilityElectability
DemocratClinton845363
DemocratSanders16850
RepublicanBush7343
RepublicanCruz8225
RepublicanRubio321341
RepublicanTrump511835

PredictWise aggregates information from various sources, including multiple betting markets as well as polling data. I don’t know which one is better. I do know that if you think PredictIt is wrong about any of these numbers, then you can go there and place a bet. Since PredictWise is an aggregate, there’s no correspondingly obvious way to make money off of it. If you do think the PredictWise numbers are way off, then it’s probably worth looking around at the various betting markets to see if there are bets you should be making: since PredictWise got its values in large part from these markets, there may be.

To me, the most interesting numbers are Trump’s. Many of my lefty friends are salivating over the prospect of his getting the nomination, because they think he’s unelectable. PredictIt disagrees, but PredictWise agrees. I don’t know what to make of that, but it remains true that, if you’re confident Trump is unelectable, you have a chance to make some money over on PredictIt.

My old friend John Stalker, who is an extremely smart guy, made a comment on my previous post that’s worth reading. He raises one technical issue and one broader issue.

The technical point is that whether you can make money off of these bets depends on the bid-ask spread (that is, the difference in prices to buy or sell contracts). That’s quite right.  I would add that you should also consider the opportunity cost: if you make these bets, you’re tying up your money until August (for bets on the nomination) or November (for bets on the general election). In deciding whether a bet is worthwhile, you should compare it to whatever investment you would otherwise have made with that money.

John’s broader claim is that “electability” as that term is generally understood in this context means something different from the conditional probabilities I’m calculating:

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.

You should read the rest yourself.

I think that I disagree, at least for the purposes that I’m primarily interested in. As I mentioned, I’m thinking about my friends who hope that Trump gets the nomination because it’ll sweep a Democrat into the White House. I think that they mean (or at least, they should mean) precisely the conditional probability I’ve calculated. I think that they’re claiming that a world in which Trump gets the nomination (with whatever other events or changes go along with that) is a world in which the Democrat wins the Presidency. That’s what my conditional probabilities are about.

But as I said, John’s an extremely smart guy, so maybe he’s right and I’m wrong.

### Ted Bunn

I am chair of the physics department at the University of Richmond. In addition to teaching a variety of undergraduate physics courses, I work on a variety of research projects in cosmology, the study of the origin, structure, and evolution of the Universe. University of Richmond undergraduates are involved in all aspects of this research. If you want to know more about my research, ask me!

## 8 thoughts on “Electability update”

1. The common perception, particularly among the Left, is that Trump is a buffoon. This is true. What is not true is that he is the worst of the bunch. He gets a lot of press because of his antics, but if you compare the positions, he is the leftmost of the Republican candidates. A very low bar, to be sure.

There is an episode of All In The Family (probably the best sitcom ever made) from the 1970s which revolves around the presidential election. The punch line of the entire episode was the Archie entered Ronald Reagan as a write-in vote. The laughter brought the house down. It was a joke. Then.

As such, it wouldn’t surprise me if Trump wins.

2. Timothy Savage says:

I’m with the Stalk on this one. I don’t think the betting markets are as good predictors in this case than more tried-and-true models of voter behavior. Now Trump is a very unconventional candidate, so you could argue that the old models don’t apply to him. But Stalk’s point about the ability to shift position to the general are well-taken. Trump has had very consistent positions on a number of positions long before he decided to enter politics. Moreover, his name recognition is 100% and he’s been in the public eye for decades, so most people already have well-developed views of him that are unlikely to change drastically based on the primary results.

So if Trump can’t appeal to a broader set of voters, his only chance of winning would be to change the makeup of the electorate. His base of voters is whites without a college education, who traditionally do not have high turnout numbers. Fivethirtyeight.com has a very nice tool where you can fiddle with turnout numbers to see how the election swings.
http://projects.fivethirtyeight.com/2016-swing-the-election/

Trump would need a significant increase in both the numbers of non-college educated whites voting AND the percentage of them voting Republican, and/or a significant drop in the number of blacks and Latinos to have a chance to win. The former would require the kind of retail, get-out-the-vote effort that Trump lacks (and which both Obama and Ted Cruz excel at). The latter seems unlikely given the strong emotions that Trump invokes, particularly among Hispanics.

That being said, I am certainly not one of those liberals who hopes for a Trump victory to propel a Democrat to the White House. The most important thing, in my view, is that both parties nominate people who, even if we disagree with their policies, could at least be counted on to not drive the country off a cliff. Trump, with his pre-WWII isolationist views, poses a risk that we cannot afford.

3. There are (at least) two different issues here. One is whether the futures markets are reliable indicators. The other is whether the conditional probabilities are the correct things to calculate to assess electability. John and I differ on the latter: even if the futures markets are reliable measures of some sort of probability, he doesn’t think that what I’m doing with them is the right thing.

On the former question, I’m not one of those people who believes the futures markets are infallible. I think that they’re one particular distillation of conventional wisdom, with all the associated advantages and drawbacks. I’m interested in them primarily because, unlike most polling data, they allow a calculation of those conditional probabilities.

The main thing I want is a rhetorical point I can make against those who hope Trump gets the nomination because they’re sure he’s unelectable. I claim that, whatever the flaws in the futures market, they provide this: to anyone who claims this, I can say, “Wanna bet?” If you’re confident that Trump is unelectable, then you can make money off of that conviction.

4. Timothy Savage says:

While I can’t claim to be as good as math as you, I still question the assumptions behind your conditional probability. The chances of any given candidate winning the presidency after getting nominated is strongly correlated to who their opponent is. The betting markets you’re citing don’t take that into account. Pollsters, on the other hand, do:
http://www.realclearpolitics.com/epolls/2016/president/2016_presidential_race.html

I think a more accurate conditional probability would be to calculate the chances of each individual matchup (Trump v. Clinton, Trump v. Sanders, Rubio v. Sanders, etc.) and then multiply that times each candidates chances of prevailing in that matchup, and aggregate the results. It would be a lot of work, though.

5. The opponent is certainly important.

I remember when Carter became president. I remember someone saying “Reagan would have carried Texas”, meaning that if Reagan, rather then Gerald Ford, had been the Republican candidate, then Carter would not have done as well.

While I can see where people are coming from when they say they would like Trump to be the Republican nominee because he is unelectable, thus ensuring a Democratic win, I don’t think that he is unelectable at all. When they were starting out, Schwarzenegger and Reagan were considered to be jokes by many.

Anyone who thinks that Trump is unelectable is vastly overestimating the US electorate.

6. Tim — You’re quite right that the probability of a candidate winning depends on the opponent, and that one way to calculate that probability would be a weighted average of the candidate beating each opponent:

P(Trump wins) = P(Trump beats Clinton)*P(Clinton is the opponent) + P(Trump beats Sanders)*P(Sanders is the opponent) + ….

But I don’t know of any good way to estimate all of those probabilities. There is polling data for various head-to-head matchups, but those don’t tell you about probabilities of various outcomes.

Fortunately, you don’t need all of those individual probabilities to get the overall probability of victory. To be precise, you can get the opinion of the bettors in the prediction markets about that probability, simply by asking them what odds they would be willing to accept for various bets. If a bettor is willing to bet that Trump will win the election at odds of 2:1, they’re saying that they believe that there’s a 1/3 chance that he’ll win. They’re making a claim about that complicated probability sum you mentioned, but you don’t need to know or think about all of those ingredients to understand the final probability.

Suppose that I say that the Red Sox have a 40% probability of winning next year’s World Series. You could write that probability as a messy sum: it’s

P(Red Sox beat Mets in WS)*P(Red Sox and Mets both make it to WS) + P(Red Sox beat Phillies in WS)*P(Red Sox and Phillies both make it to WS) + …

That’s all true, but I don’t need all that complication in order to talk about the probability that the Sox win the series.

The specific claim I’m making is this: if you believed (as of Monday) that Trump’s conditional probability of winning the election, given that he wins the nomination, is significantly different from 62%, then you could have made money off of that conviction by placing suitable bets at PredictIt at odds that are in your favor.

7. “The main thing I want is a rhetorical point I can make against those who hope Trump gets the nomination because they’re sure he’s unelectable.” That’s what I was afraid you were doing. I believe any attempt to do this using conditional probabilities is doomed.

The conditional probabilities reflect the betting markets’ best guess of future events in the world we really live in, one where primary voters and caucus participants choose their parties’ nominees. When I think about who I hope they nominate I am answering a question about a different world, one where I get to pick their nominees for them. In that calculation I will presumably view electability favourably for the party I hope wins in November and unfavourably for the party I hope loses.

In practice I’m with Tim on this one, and wouldn’t try to game the system by choosing someone I thought would make a terrible president, but that’s not really the issue here. Neither is the issue the prediction markets’ skill, or lack thereof, in assigning probabilities to future events. The issue is that when I’m deciding who I hope the parties nominate I’m imagining a world where I get to decide that, because otherwise the question doesn’t make much sense. That world is very different from a world where the candidates have to persuade millions of other people to vote for them, and only reach the general election if they have succeeded in doing that. It’s the latter world which the prediction markets are attempting to predict.

The standard political science model of elections is what in physics terms we might call a hidden variables theory. Candidates are described by some directly observable variables, like experience and ideological positions, and some hidden variables which represent those aspects of candidate quality which we can’t observe except through their effect on election outcomes. Every election provides additional data points for estimating those variables, via Bayes’ Theorem.

“Electability”, to the extent that it means anything, is a proxy for the candidate quality variables, both the directly measurable ones like experience, and these hidden variables. For most of these candidates we have very few measurements. Clinton has contested a general election for the Senate and a presidential primary. Trump has never run for anything. The information we get from the outcome of this years’ primaries is therefore quite valuable, particularly if that outcome is unexpected.

My estimate of Carson’s electability, for example, will change enormously if he wins the nomination. When the prediction markets evaluate his odds in the general election what they are doing, or at least should be doing, is estimating that probability based on what they know now plus an imagined additional measurement: his presumed Republican primary win. When I say today that I don’t think he’s very electable I’m basing that on our present state of knowledge, where she’s never won an election for anything and doesn’t seem likely to.

In short, I don’t believe one can freely mix the language of hope with that of probability theory and expect all the resulting statements to be meaningful.

8. “When I think about who I hope they nominate I am answering a question about a different world, one where I get to pick their nominees for them.”

Then I agree that the conditional probabilities I calculate are not right for you. But I still think that they’re right for a certain category of people. When lefties I know say that they hope Trump is the nominee because the Democrats will beat him, I don’t think they’re saying, “I wish that the world were a different sort of place, in which Trump wins the nomination.” They’re saying, “On averaging over all the unknown possible ways the world might be (with their associated probabilities), the outcomes in which Trump is the nominee are better for my party than the outcomes in which Trump is not the nominee.”

Of course, I don’t know for sure that that’s what they’re thinking, but I think it is. If they’re thinking the way you suggest, then I agree that you’re right.

To be more specific, for someone who is thinking of voting strategically in the opposing party’s primary (e.g., voting for Trump to help the Democrats), my model is closer to the right one than yours. That person is considering what marginal change they should be trying to effect in the world as it actually is, not imagining a world in which they got to choose the nominee.

Like you, I wouldn’t vote strategically in this way, for at least two reasons:

1. I don’t trust either the prediction markets or my own instincts well enough to be sure I’d do it right.
2. Such an action doesn’t feel ethical to me. Casting a vote for, e.g., Donald Trump is, in my opinion, an unethical act for reasons that are not merely utilitarian.