Posterior Perry-bility: A (semi-serious) Bayesian update of Rick Perry

October 13, 2011

As we continue to adjust the trims on our Who Will Be the Nominee© model, let’s assess Rick Perry’s chances of the GOP nomination, given his track record in the first four debates.

If we go with the traditional political science wisdom that campaigns don’t matter that much (good review of topic here), then  new information we receive is not affecting the outcome so much as  just revealing the true state of the world.

And that means it’s clearly time to whip out some Bayesian analysis! Let’s get right to the priors.

Priors (as of 9/6, before first debate)

Probability (Perry is GOP nominee) = 39% = .39  [estimated from intrade]

Probability (Perry is not GOP nominee (i.e. Loser Perry)) = 61% = .61 [inverse of above]

Probability (Nominee Perry has four mediocre-at-best debates) = 20% = .20 [feels about right]

Probability (Loser Perry has four mediocre-at-best debates ) = 40% = .40 [again, feels about right]

Event

Perry has had four mediocre-at-best-debates.

At the Reagan Library (/7), he failed to impress and looked unprepared on Social Security. At the Tea Party Express debate (9/12), he was hammered on HPV and did not recover well. In Orlando at the Fox debate (9/22), his performance was described by the Weekly Standard as “disqualifying.” At Dartmouth (10/11), he announced he had no jobs plan, gave the impression he had disappeared, and then spent his post-debate meet and greet at Beta Theta Pi riffing on America’s 16th century revolution.

Question

Given this observed event, what is our updated probability that Perry is the GOP nominee?

Solution

Use Bayesian inference.

Probability Perry is GOP nominee given four mediocre-at-best-debates = ((Probability he has four mediocre debates  if he is the nominee)(Probability he is the nominee)) / (((Probability he has four mediocre debates given he is the nominee) (Probability he is the nominee)) + ((Probability he has four mediocre debates if he is not the nominee) (Probability he is not the nominee)))

Written in simple notation:

P(Nom |E1) = ( P(E 1| Nom) P(Nom) ) / (( P(E1 | Nom) P(Nom) ) + (P(E1 | Loser) P(Loser)))

P(Nom|E1) = (.20)(.39 ) / ((.20) (.39) + (.4) (.61))

P(Nom|E1) = .24

Answer

Updated probability Perry is GOP nominee given four mediocre debate performances = 24%

Discussion

Still viable, confirming some recent wisdom.  But looking a lot less like the GOP nominee than he did six weeks ago. Given that he is currently trading around 11% on Intrade, the above analysis suggests the market might be overreacting, creating an opportunity for some value investing.

Obviously, you can quibble with the estimated priors. Who the hell am I to assign specific percentages to debate-failure probabilities? And that’s the key theoretical question raised by the analysis: what’s the true gap between the probability of the nominee having four bad debates and the probability of a non-nominee having four bad debates. My priors say it’s about twice as likely. Yours may differ, even substantially.

But if you accept the priors as reasonable — that nominee Perry would have about a 1 in 5 chance of four mediocre debates, and Loser Perry about double that chance — then the conclusion is that Perry still has a reasonable likelihood of being the nominee, but the probability has decreased a fair amount.

Someone check my math. Everyone assess my priors.

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