# Will a Third-Party Candidate Get 10% Support for Governor of Virginia?

Doug Mataconis is impressed that third-party candidate Robert Sarvis is polling as high as 10% in the Virginia Governor’s race.

Color me skeptical, not because of anything specific to Sarvis but because of statistics. As the true level of candidate’s support gets farther in either direction from 50%, polls become increasingly less accurate. To quote myself from a post that lays out the math in more detail:

It is simply harder to predict events that are unlikely than events which are likely. If a fair coin is being flipped over and over and you have to guess on which particular flip it will come up heads, you’ve got a 50-50 shot of winning the game. But if the same game is played with an unbalanced coin that comes up heads only 1% of the time, you will almost certainly not guess the right flip, even if you are allowed to play many times. Indeed, any system you might use to predict when the elusive heads result will occur will be less accurate over time than simply predicting that the coin will never come up heads no matter how many times it is flipped.

As I show in the linked post, a 90% accurate poll including a candidate who actually has 1% support will estimate his/her support at 11%. And when your support is really low, most errors in estimation can only go in one direction: Upward.

Sarvis could matter in the tight Virginia Governor’s race even if he only nets a few percent of the vote. But the likelihood that he truly has the support of 10% of Virginia voters is low.

1. dave schutz says

Terry Mack and Cooch are both kinda revolting. I’m thinking of voting for Sarvis, or just not voting the top of the ticket.

2. Ken Doran says

I believe that third party candidates routinely poll better than they end up achieving on election day. While this analysis is one reason, there are others as well. When I tell a pollster that I plan to vote for Mr. Thirdparty, my message may more precisely be that he is the one I would most prefer to see in office. Come election day, if he clearly has no chance, and I have any preference between one and two, that is likely where my vote will go.

3. Dead or In Jail says

There are the makings of an interest point here but, as it stands, this is just a banal truism about statistical analysis and American political behavior. (Outliers are prone to mismeasurement; also 3rd party support declines precipitously on Election Day.)

Does it matter that Sarvis’s personal qualifications (not even including his super-hot wife) are exceptional?

Does it matter that the “realistic” major party alternatives are morally disabled?

And, on a public policy blog where there are at least two(2) leading experts on American Drug Policy, Sarvis is proposing solutions that could significantly ameliorate (but not solve) the problems associated with our current drug laws?

• Ken Doran says

“Does it matter that Sarvis’s personal qualifications (not even including his super-hot wife) are exceptional?” To the question posed by Keith, no it does not. Super-hot, you say; may have to research that aspect of the issue on Google Images.

• Dead or In Jail says

You can see a picture of Sarvis’s beautiful family in my original post.

I was really trying to goad Dr. Humphreys or even Dr. Kleiman into commenting on Sarvis’s drug policy proposals. While it’s nowhere as detailed as a white paper, it is more fleshed out than a typical candidate’s website.

• Ken Rhodes says

From your link: He has earned degrees in mathematics from Harvard University and the University of Cambridge, a J.D. from N.Y.U. School of Law, and a Master’s in economics from George Mason University. He has a diverse professional background, with experience as an entrepreneur and small-business owner, a software engineer and mobile-app developer, a math teacher, and a lawyer. Rob is married to a pediatrician from Greenville, MS, with whom he is raising two beautiful children in Annandale, Virginia.

Hey, based on that brief bio, I’d vote for him over anybody I voted for in Virginia in a LONG time. For one thing, he’s apparently a lot SMARTER than any of them.

• Fred says

Why does this guy have so much trouble holding a job? Hmmm?;)

4. rachelrachel says

Candidate preference polls are very accurate, a lot better than 90%. Polls done right before election day are very close to the actual election results.

Third-party candidates tend to poll higher earlier in the season and lower as election day draws near.

In rare circumstances a third-party candidate might win an election. It’s possible that will happen in the Virginia race, but the odds are against it.

• Keith Humphreys says

rachelrachel wrote Candidate preference polls are very accurate, a lot better than 90%.

It depends how large the samples are and how well the poll is designed – many polls use small samples and/or are poorly designed, particularly at the state, county and city level of politics. For a candidate with between 40-60% support a 90% accurate poll is pretty good at estimating support.

Note also that for a 95% accurate poll, a candidate whose real support is 1% will typically poll as having 5%.

• Anonymous says

Wow, I can’t believe the level of statistical innumeracy here. The phrase “90% accurate poll” isn’t even meaningful. The absolute error statistical error bars on the % go down as the % gets close to 0 or 100. (Var(x)=p(1-p)/N, as you learn in the first week of a high school probability course.)
The real issue here is not statistical. People say they’ll vote 3d party but then when it comes down to it, they don’t, for obvious reasons.

• Ken Rhodes says

If you’re gonna make fun of our statistical chops, shouldn’t you show the variance as the product of pqN, rather than the quotient of pq/N?

• Keith Humphreys says

Guess he was sleeping that day in his high school probability course…

• Anonymous says

Dude, we’re talking about averages, not totals. Your formula would have Var of a percent diverge for large N.

• RichardC says

I would agree with this, *especially* in the case of a low-support candidate.
The idea of a poll being “90% accurate” in the sense of this statistical
analysis is massively implausible: false positives and false negatives are
very different. And if there’s a third-party candidate, then it seems
very likely to me that they know quite a bit about what’s going on, and are
describing their intention accurately.

From my recollection of presidential campaigns involving Ross Perot and Ralph
Nader, it seemed to me that the polling numbers at the end of the campaign
were quite close to the final result, so I don’t see evidence for the idea
that polls have this level of inaccuracy. Now it’s quite plausible that,
under a first-past-the-post voting system, many people whose first choice
is a third-party candidate will decide close to the election that one of
the major-party candidates is going to win so they’ll vote tactically for the
lesser of two evils. But that has nothing to do with polling inaccuracy
or Bayesian statistics.

5. James Wimberley says

Perhaps pollsters should routinely include a dummy candidate, Cyrus Q. Hackenberger, who isn´t running. His polled support is pure noise; nobody will vote for him, as he isn~t on the ballot. But his score would give an indication of the noisiness of the poll.

Question. In the US, third-party candidates are only occasionally important (Teddy rooevelt, Ross Perot, Ralph Nader). In proportional representation systems they can matter a lot routinely.

So how far does Keith´s warning apply to the polls for today´s election in Germany? It´s a matter of consequence whether the neoliberal FDP gets over 5% or not. If it drops below, it will not get any party-list seats in the Bundestag and will not be able to form a coalition with Merkel´s CDU. Recent polls are all very close to 5% (range in September 4%-6%). FDP ministers have been leading a campaign against the popular Renewable Energy Act and particularly the feed-in tariffs which have created Germany´s splendid solar and wind boom, so I´m hoping for 4.99% and purple faces.

• Warren Terra says

Or, rather than name the options, the pollster could ask the respondent to name their preference. Party labels would be accepted as answers; ideological labels might also be (though there could be a bit more room for ambiguity).

• Keith Humphreys says

One thing I would be interested to know is whether pollsters in countries where third parties routinely matter use larger samples to accommodate this reality. In the U.S., if you are budget conscious you statistically power a poll to tell you how the two major party candidates are doing. That makes for poor estimates of the popularity of off-brand candidates, but who cares when they have no chance? But it matters a lot to get the small fry right in countries such as Germany, so perhaps pollsters use the larger samples that would provide the power to do this (Not that sample size is the only way to increase power, but it is the most common way).

• Katja says

Yes and no. You can see the data for German federal election polls on this page. Allensbach, Emnid, FORSA, Forschungsgruppe Wahlen, GMS, Infratest dimap, and INSA are the names of the major pollsters. You can click on them to see a history of their polls over the past years. The column “Befragte” (Respondents) on each pollster’s page will give you the sample size for each poll. As you can see, the sample sizes ranges from around 1,000 voters to well over 2,000. Because the margin of error is inversely proportional to the square root of the sample size, you will hit diminishing returns pretty fast.

There’s also limited value to a low margin of error for these polls. A fairly large number of German voters are undecided who to vote for even shortly before an election; also, many German voters engage in tactical voting where they don’t necessarily vote to maximize their preferred party’s chance of winning, but also their preferred coalition’s chance of happening. This frequently takes the form of voters “lending” their votes to a small party that is struggling to meet the 5% threshold. All this means that there’s a lot of unavoidable noise to election polls that even a sample size of 100% couldn’t eliminate.

• Keith Humphreys says

@Katja: Is margin of error in polls the same for each candidate regardless of their level of support?

p.s. FWIW the polls cited in Mataconis’ article are between 750-1000 respondents.

• Katja says

No, margin of error is not the same regardless of level of support and generally cannot be (I’m assuming you mean parties instead of candidates, as support for candidates is not very important in a proportional or MMP system). For example, the last Infratest poll cited a margin of error of 1.4% for a party around 5% and a margin of error of 3% of for a party around 50% (I haven’t verified whether these numbers are accurate [1]).

[1] Obviously, each pollster has its own methodology to try and arrive at a representative sample (which is more difficult than it may appear to be), so that things like this don’t happen. Also, polling methodology can vary considerably by country, too.

• Keith Humphreys says

Thanks Katja, that was what I assumed but it is helpful to know from a voice of reason who really ought to be a blogger.

• James Wimberley says

Stop press: My hopes were answered! The FDP got 4.8% and is out. The new nationalist AfD party – Poujadist raher than fascist SFIK – just failed to make the cut as well. Merkel missed an absolute majority and is expected to seek a ¨grand coalition¨ with the Social Democrats. These are a little (not much) wetter than her CDU on Euro austerity and quite a lot greener, so it´s definitely a change for the better.

• Ken Rhodes says

You go, James!

I like 4.8% a LOT better than your wished-for 4.99%. That number of yours looks dangerously close to being raised .01 by a recount. A difference of minus .2% looks pretty safe.

• Warren Terra says

Funny. But, as is so often the case, this bit of satire has a Poe’s Law problem: it’s quite possible you could genuinely get this result.

6. says