Statistician super-star and FiveThirtyEight editor Nate Silver has gained fame for his spot-on predictions around elections; he had accurate predictions for all 50 states during the 2012 presidential election. While it seems that Silver has the power of precognition, he actually relies on refined statistical methods—including weighting various political polls—to make predictive models.
Recently, Silver and FiveThirtyEight put out a forecast for the 2014 Senate race which examines the races on a probabilistic basis. Silver’s analysis, which simply sums the probabilities of each side winning all its races, projects that the Democrats are slightly more likely to lose control of the chamber than to retain it.
Lawrence W. Robinson, Professor of Operations Management at Cornell University’s Johnson Graduate School of Management took this research one step further by adding Monte Carlo simulation to the mix. Robinson set out to determine, in his words, “the probability that the Democrats hold at least 50 seats in the new Senate.” Only 50 seats are needed because Joe Biden will, in his role as president pro tempore of the Senate, break ties in the Democrats’ favor. “What we really want to know is, what chance will the Democrats have to retain control”?
After using @RISK to crunch the numbers, Robinson found that the Democrats have only a 41% chance of retaining control of the Senate.
While Silver warned in previous articles that to assume races are uncorrelated is “dubious,” and that Monte Carlo simulations requires variables to be uncorrelated, Robinson demonstrated that it’s in fact very possible to include correlation in Monte Carlo analyses.
By creating a “lower bound” (zero correlation) and an “upper bound” (total correlation) Robinson showed that Democrats’ chances of retaining control only hovers somewhere between the aforementioned 41% and 50%.
With the upper and lower bounds in place, Robinson went on to create a model that allows the coefficient of correlation between every pair of elections to vary between 0% and 100%, and found the probability that the Democrats will hold the Senate for each different correlation coefficient value.
As Robinson says, “It would be very difficult to determine the correlations among all the different Senate races. However, if the coefficient of correlation is anywhere in the wide range between 20% and 85%, then the probability that the Democrats will retain control of the Senate (i.e., hold 50 or more seats) will be in somewhere in the very narrow band of 45% ± 0.1%.”
Stay tuned as the mid-term Senate race approaches this fall—Robinson plans to model more nuanced and data-rich predictions as the election nears.