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Bayes’ Rule in the Presidential Election

Last year, Republican candidate Ted Cruz claimed that more moderate Republican candidates have less chance of winning the election than do less moderate candidates. Recent research conducted by the American Political Science Review Journal highlights the inaccuracy of Cruz’s claim and displays that moderation is rewarded during elections. The Washington Post has used Bayes’ Rule and two prediction markets ─ Betfair’s Republican Nomination Market and Next President Market ─ to predict the Republican candidates’ likelihoods of winning the presidential election given that they first win the Republican nomination. The Washington Post’s findings support the research conducted by the political science journal.

Betfair, a prediction market, predicted, for example, that there is a 7.5% chance that Rubio will be elected president and a 20% chance that he wins the Republican nomination. The conditional probability that Rubio will be elected president given that he wins the Republican nomination is as follows:

(Pr(Elected Pres)*Pr(Wins GOP Nomination / Elected Pres)) / (Pr(Wins GOP Nomin)

In this case, Bayes’ rule would indicate that the probability that Rubio wins the presidential election given that he first wins the Republican nomination would be (0.075)(1) / (0.20), which equals a 37.5% chance (Washington Post). Similar calculations for the other candidates support the research conducted by the American Political Science Review Journal. Rubio, for example, is more conservative that Bush, and Rubio is less likely than is Bush to win the presidential election if he wins the Republican nomination. This demonstrates that a more conservative candidate has a greater chance of winning the presidential election than a less conservative candidate has. Similar results appear in Bayes’ rule calculations for the Democratic candidates: Sanders, who is more liberal than Clinton, is less likely to win the general election than is Clinton given that he wins the Democratic nomination first, again supporting the research conducted by the American Political Science Review Journal.

Bayes’ rule, or conditional probability, is useful in predicting the outcome of one event given that you have observed another. Bayes’ rule will most likely be used throughout the entire election season to determine chances of candidates as the election gets closer.

SOURCES:

https://www.washingtonpost.com/blogs/monkey-cage/wp/2015/09/25/if-republicans-nominate-a-strong-conservative-it-could-hurt-them-on-election-day-a-lot/

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=208466&fileId=S0003055402004276

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