Veni Quid Veniat

      The first major Republican presidential primary debate takes place in only three days. In an attempt to avoid hosting a circus, the debate’s sponsor, Fox News, capped the number of participants at ten, to be selected using an aggregate of the five most recent reliable polls - the top ten would be included; the bottom seven left out. The rationale is obvious: with seventeen candidates on stage, some of them with no chance, even in their own minds, of actually winning the presidency, none of the candidates would have time to convey any sort of message. After watching the debate, viewers would be left knowing just as little about the candidates as they did before.

     As good as the argument for limiting the field is, there is an argument on the other side. The polls going into the average are generally very imprecise, with large margins of error. When distinguishing between the tenth and eleventh place candidate, a few percentage points could make an enormous difference; if the polling average includes polls with a six-point margin of error, how sure can we be that we really got the top ten?

      The answer is that we can't be certain, but we can be reasonably sure, as long as we do the calculation correctly. Taking the weighted average of the polls, accounting for the margin of error of each one (strangely enough, Real Clear Politics, one of the leading sources of aggregate polls, does not do this), it's possible to guess at the actual value with much more precision than any one of the polls going into the analysis, as shown in the graph below (the red line marks the tenth candidate).


     It should be clear that, although it's still difficult to make a noticeable difference between the tenth (Christie) and eleventh (Perry) candidates, the margin of error has dropped to 1.95 percentage points - enough that the distinction between one candidate and another, even in the middle of the pack, is not entirely arbitrary. It is, for example, possible to say with almost complete certainty that Cruz, the leading candidate from the lower tier, is polling well ahead of Graham, whereas this wasn't necessarily possible with every poll that went into the analysis.

      It should also be noted that the values calculated here don't match those from RCP's averaged polls, and it does change the order: RCP incorrectly has Walker slightly ahead of Bush, whereas in reality the opposite is the case. As long as Fox does its due diligence and avoids falling into elementary errors, we can be reasonably certain that the ten candidates on stage will be the top ten candidates in national polls. Whether those national polls have any meaning at all this early in the contest remains to be seen, but the process, at least, is sound.