The Complicated Math of Last Week's Republican Debates

On August 6th, FOX News held the first debates for the Republican Party primaries. But how did they pick the candidates? Was it fair? Shortly before the debate, the New York Times "The Upshot" section predicted who would be included in each debate and discussed the impact that sampling errors could have on who made it onto the prime time stage. 

In case you were busy watching Project Runway, allow us to recap the line-ups for last week's debates. There were two rounds; a ten candidate main event and a smaller seven candidate round earlier in the evening. The candidates in the main event were businessman Donald Trump, former Florida Gov. Jeb Bush, Wisconsin Gov. Scott Walker, former Arkansas Gov. Mike Huckabee, retired neurosurgeon Ben Carson, Texas Sen. Ted Cruz, Florida Sen. Marco Rubio, Kentucky Sen. Rand Paul, New Jersey Gov. Chris Christie, and Ohio Gov. John Kasich. In the smaller round, the candidates are former Texas Gov. Rick Perry, former Pennsylvania Sen. Rick Santorum, Louisiana Gov. Bobby Jindal, former HP head Carly Fiorina, South Carolina Sen. Lindsey Graham, former New York Gov. George Pataki, and former Virginia Gov. Jim Gilmore.

How did FOX arrive at these line-ups? According to their press release from this May, the top ten slots were filled by candidates who placed "in the top 10 of an average of the five most recent national polls, as recognized by FOX News leading up to August 4th at 5 PM/ET. Such polling must be conducted by major, nationally recognized organizations that use standard methodological techniques." The national polls FOX News ultimately chose were those of CBS News, Bloomberg News (results shown below), Monmouth University, Quinnipiac University, as well as one FOX themselves conducted
. From there they chose the top ten and the bottom seven by averaging the results of each candidate in each poll. 

As The Upshot notes, however, there is a significant problem with the accuracy of this method. Each of these polls has a margin of error of +- 3.5%. This means that Rick Perry, who leads the smaller debate after taking 1.8% of the responses, might actually have a larger number (up to 5.3%), which would put him in the top ten. The candidate in the top ten with the lowest percentage is John Kasich, with 3.2% of the responses going to him. If Rick Perry were more popular, Kasich and Perry may be in opposite positions, with Perry in the top ten and Kasich in the bottom seven. In fact, if the margin of error were to be taken to the extreme, the only candidates that could stay in the top ten are Trump, Bush, and Walker. 

Is this system fair? That depends on how fair you find random chance. Sampling errors aren't a secret among those who work with data and, as this post on explains, using national polls is more effective than using early endorsements, early Iowa polls, and how much money the candidates can raise to measure who will win the general election despite the inherent flaws it presents.

A Foster