From a purely probabilistic point of view, would Hillary Clinton dropping out of the race improve the democrats chance of beating Donald Trump? (Spoiler: No)

The prediction market site PredictIt has these four securities based on the outcome of the presidential election.

Assuming that the republican and democratic tickets don’t change, and that one of those parties wins the election, these securities will all have the same outcome and thus the same prices. So why do we have four securities? Because six months ago, it was less clear what the tickets would look like and so these securities had different pricing.

As part of the agreement PredictIt has with the CFTC, in order to allow real-money trading they limit each security to at most 5000 traders. When the 5000 limit is reached, no one else can buy into the security until some other trader sells all of his or her shares. The limit has been reached for Clinton and Trump on the “Who will win” security but not on the other securities. Not being able to buy Clinton or Trump might affect the predictive power of the security but it seems that isn’t the case because the “Who will win” security has closely tracked the “Which party will win” pretty closely from the convention until a week ago.
What happened a week ago? Let’s look at the charts.

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The Clinton security dropped down to 63¢ on September 11th (when Clinton had to leave the 9/11 ceremony and later revealed she had pneumonia) while the democratic security cropped only to 67¢. This mirrors the “Clinton will drop out by the end of September” security.

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These charts give us a little insight into the question: Given Clinton’s high negatives, would Clinton dropping out of the race and being replaced by another democratic candidate raise or lower the chances of the democrats winning? The probability that the democrat wins given that Clinton drops out is equal to the probability that democrats win minus the probability of Clinton winning out all over that probability of dropping out, or, using the prices on Sept 12, (.69-.64)/.12 = 42%, so democrats are significantly better off if Hillary stays in.

These calculations should be taken with several grains of salt, because the Predicit numbers are only rough approximations due to transaction costs.

Lance Fortnow is a professor and chair at the School of Computer Science at the Georgia Tech College of Computing