President Paul Ryan
I am writing about an article titled “What are Paul Ryan’s chances of Becoming President?” This article was inspired by a mistake that Mitt Romney made when announcing his counterpart. He claimed that Paul Ryan would be the next president of America instead of vice president. This slip due to Romney’s overwhelming campaign caused Nate Silver, a New York Times writer, to wonder what the actual chances are that Paul Ryan would be a president of the United States. Silver collected data on the vice-presidents since 1900. In this data, he double counted vice presidents that were elected twice. There were 27 vice presidents since 1900 excluding Biden because he has not had a chance to run for president yet. This is because Obama ran for re-election this year and Biden was not going to run against him instead of with him. Also there were 28 runners up vise presidents since 1900. This is because Palin could have run for president in this election, but she chose not to.
Given the data in this article and knowledge of Bayes’ Theorem from class, we can calculate many different probabilities. Let’s calculate the probability that a candidate was a vice president given that they ran for president. Say P(W) is the probability that a candidate was elected to be vice president and P(L) is the probability that a candidate was not elected to be vice president (this is assuming that the candidate in question actually ran for vice presidency and was on the final ballot). Let’s also say that P(R) is the probability that a candidate (that was on the final presidential ballot as a vice president) will run for presidency. Therefore we are looking for P(W|R). Using Bayes’ Theorem, we know that P(W|R)= P(R|W)P(W)/[ P(R|W)P(W)+ P(R|L)P(L)]. From the article, we know that P(R|W)= the probability that a candidate will run for presidency given that they were vice president= 21/27. For simplicity of this model, we will assume that a candidate has a 50% chance of being elected if they are on the final ballot. I know that this is very unrealistic, but it is necessary to apply Bayes’ theorem. Also P(R|L)= the probability that a candidate will run for presidency given that they lost the election for vice president= 9/28. Here there are 28 vice presidents in question because Palin had the chance to run this past election when Biden did not, so she is included. Therefore P(W|R)= (21/27*.5)/[(21/27*.5)+(9/28*.5)]= .70758, which is about 70.76%. This is a very high percentage, so it is very likely that a candidate was elected vice president given that they ran for president. This is because a candidate is way more likely to run for president if they were elected vice president as opposed to not winning the election. So, if in the future Romney’s slip was turns out to be true, Romney and Ryan most likely won this year’s election.
But, today we know that this is not true. Obama won the election. So what is the probability that a candidate was not vice president given that they ran for presidency? P(L|R)= P(R|L)P(L)/[ P(R|L)P(L) + P(R|W)P(W)]. Given the numbers from above, P(L|R)= (9/28*.5)/[ (9/28*.5)+ (21/27*.5)]=.29242. This is about 29.24%. Therefore it is unlikely that a candidate that ran for presidency was not voted for vice presidency. This probability is the opposite of the previous probability we found and therefore they sum of them equals 1. This is because given that a candidate (that was on the final ballot for vice presidency) runs for presidency, they can either win the election or loose the election for vice presidency. These two options partition the space. All in all, the statistics that Silver collected show that there is a much higher chance for a vice president to run for presidency (P(R|W)=21/27) as opposed to a candidate that was not elected to be vice president (P(R|L)=9/28). Therefore the odds are lowered for Ryan as president, but it is still possible. So, we will just have to wait until the future to see what Ryan decides.
-MC