Table 1 was not intended to communicate the average of averages, it was only illustrating the sample space. KC, GVT, and others did not perform any analysis on the average of averages.

]]>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.

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.

]]>I did read your working paper quite carefully, and found it quite clear. There seems to me to be no room for doubt that the procedure laid out in Table 1 (which I refer to as an “average of averages”, although I have no objection to calling it something else such as an “average of probabilities”) bears no relation to the work of Koehler and Conley and virtually no relation to the work of Gilovich et al.

]]>That box purports to be an explanation of the argument in the working paper. If it’s not, then you should urge the New York Times to publish a correction.

]]>just came across your two posts on google. I posted a note on your other post.

The statistic is computed for a single sequence, and the test is performed for a single player, so it it more natural than described here.

There is no analysis of an average of ratios.

We have a primer that addresses your concerns, here it is:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2728151

just came across your post on google.

unfortunately our paper was not written in a way that the issues would be clear in quick perusal, and depended a bit on our earlier papers, which we referenced.

in case you are interested, we have a primer that addresses your question, here it is:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2728151

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.

]]>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.

]]>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.

]]>