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The Math Problem Behind Ranking The Top 10 GOP Candidates

Former U.S. Sen. Rick Santorum (R-PA), shown here in a November 2011 debate, is polling poorly these days. But does that mean he shouldn't get to debate?
Scott Olson
Getty Images
Former U.S. Sen. Rick Santorum (R-PA), shown here in a November 2011 debate, is polling poorly these days. But does that mean he shouldn't get to debate?

Sixteen presidential candidates talking over each other doesn't sound much like good TV. CNN and Fox News know this, so when they air their Republican debates later this year, they'll both limit the field to 10 candidates.

Both networks will use polling data to limit the field to only the 10 most popular candidates (CNN will have a second debate featuring the also-rans). It'll cut down on the chaos, but there's a big problem with winnowing down the field this way: the lowest-rated people included in the debate might not deserve to be there.

The latest GOP presidential poll, from Quinnipiac, shows just how messy polling can be in a field this big. We've put together a chart showing how the candidates stack up against each other among Republican and Republican-leaning voters — and how much their margins of error overlap. Twenty percent of respondents said they didn't know who they'd vote for, but among the rest, here's what the breakdown looks like.

In this poll of Republican and leaning-Republican voters, there's a +/- 3.8-percentage-point margin of error, so we created bars around each estimate showing that margin of error. The message is simple: there's a lot of uncertainty about just how much support each candidate has, with so many candidates, each with such low levels of support.

(And a couple of nitpicky notes: This chart is a little bit of an oversimplification — Quinnipiac appears to have rounded everything to the nearest digit, so these ranges are approximate. Not only that, but for super-low readings like 0 or 1, statisticians might sometimes use other methods to compute margins of error, so those margins might be a little smaller at the low end of the spectrum.)

A quick stats 101 primer: A margin of error tries to capture how far off the survey's finding differs from the true thing it's trying to measure. Each margin of error comes with a "confidence interval" — a figure that tells you how reliable the results are. Quinnipiac's polls come with a 95 percent interval, meaning that if you were to perform this same survey 100 times, it would come out with a result somewhere in that +/- 3.8-percentage-point range 95 times out of 100.

In short, polls by their very nature make it difficult to know which lower-tier candidate truly has more support than another.

In this poll, Fiorina and Kasich are tied in 10th place, at 2 percent. Graham, Jindal, and Perry are all at 1 percent. If the two scheduled debates were using this poll, they would allow Fiorina and Kasich, then, while jettisoning the other three, even though this particular poll makes it impossible to tell who, in fact, has more support. Do the poll 99 more times, and in many of those polls, Perry might easily come out one or two points ahead of Fiorina or Kasich.

Of course, Fox and CNN won't be using just one poll; they'll each be using an average of several polls, which does shrink the margin of error some. But average together the most recent GOP nomination polls, and the difference between 10th, 11th, and 12th place is still miniscule, and the order of candidates changes often. In lots of polls, the bottom contenders are grouped tightly together.

Unless a few people drop out or unless there somehow becomes a clear separation between 10th and 11th places by August (when Fox will hold its debate), there's a good chance the debates will exclude someone who could or should arguably be there. (And there are also some experts who say averaging polls is a waste of time, as the National Journal wrote in 2012)

That's just one reason the 10-top-candidates approach could be flawed. There are a few other potential weaknesses as well: for one, excluding some candidates (or separating them into a debate JV squad) could easily further marginalize candidates who might prove their mettle against Rubio and Bush.

Consider Rick Santorum, who turned in strong 2011 debate performances and soon thereafter sprinted to the front of the pack, narrowly winning the Iowa caucus. Leaving out the bottom contenders eliminates that kind of possibility this time around, and relegating them to their own debate at the very least makes it far less likely.

Furthermore, not allowing the bottom candidates to debate could further advance those candidates with an early name-recognition or money advantage.

Thursday morning, political analyst Stu Rothenberg outlined in a blog post a simple fix to the GOP's overcrowded-debate problem: set up two debates, then randomly assign the candidates to one or the other.

"After all, we are talking about the first debate or the first couple of debates, not the fifth," he wrote. "Each candidate can rightly argue he or she deserves to be in the first few debates, since those televised events will be the first time many Republican voters will have the opportunity to evaluate and compare the candidates."

Eventually, he added, there could be reason to winnow the field down. But doing it too early could shut out lower-tier candidates before they have the opportunity to catch fire.

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Danielle Kurtzleben is a political correspondent assigned to NPR's Washington Desk. She appears on NPR shows, writes for the web, and is a regular on The NPR Politics Podcast. She is covering the 2020 presidential election, with particular focuses on on economic policy and gender politics.