# What is the typical error in large vote counts?

Well the EU referendum happened in the UK and there was some talk about what happens if the result is a tie, or if it is very close. Apparently, there would not be a recount unless there was a specific problem with the counting in one area. I am not interested in the legal questions of what happens if the result is close. The person who has the largest number of declared votes wins. That's how it works.

What I am interested in whether anyone has estimated the error on the final results? When people count up all the votes, they make accidental mistakes. If you counted all the votes ten times you would likely get ten different numbers which is why people do recounts to check that the result is correct.

Has anyone ever looked at data from recounts in previous elections, either in the UK or elsewhere, to estimate the sort of standard deviation that we can expect. If you do two recounts and the results differ by a hundred votes in ten thousand, is this statistically significant or is it within the expected error from human counting?

I hope the question is clear now. Please ask if it is not.

• check this link about US elections, maybe it would give you an idea :) Jun 24, 2016 at 8:33
• What error margin? All the votes are counted; the biggest one wins. Simple majority. There is no error margin. This question doesn't make sense. It's a vote, not a survey.
– TRiG
Jun 27, 2016 at 0:18
• @TRiG I don't think you understand my question. I have edited to provide a bit more explanation.
– bon
Jun 27, 2016 at 17:31
• @GautierC That doesn't answer the question. The question is about the standard deviation on the number of votes counted for each side. We do not know with absolute certainty that the number of votes stated is the correct number that were cast because there is some degree of human error in the counting process.
– bon
Jan 14, 2017 at 9:50

## Margin of Error

There is no error margin for vote counting.

Margin of error is a measurement of uncertainty that results from sampling. When votes are counted, they don't pull a random of sample of ballots to count; they count all of them. Therefore, there is no margin of error.

## Measurement Error and Research

However, there may be measurement error. This is the error introduced by measuring (counting) votes. I searched through some political science journals (through JSTOR) and didn't find anyone who has done the research you want.

This is likely because there is no good example to study. In order to do this research correctly, you would need a single election with a large number of recounts. This doesn't happen, ever. It's unlikely to have a single recount, let alone enough to generate some useful inferences.

Why not look at a large number of elections each with one recount? Because with only two observations you won't be able to tell anything useful. It's entirely possible that with only two observations, both of them are unreasonably high or low. In the best circumstance, your conclusion would only be a range of possible differences between the two vote counts ("95% of recounts resulted in a difference of between 1%-3%", for example). This doesn't tell you anything about what the true value of any of the elections are.

• What is the point of a recount then? If you do a recount and get a different result then there is an error. If you have lots of data on recounts you can calculate a standard deviation of the sort of accuracy that you expect when counting votes.
– bon
Jan 14, 2017 at 18:30
• "There is an error" is correct, but it isn't because of sampling error. I think you are using a technical term ("error margine") when you really mean something else. A recount would (hopefully) reveal other kinds of error. Jan 14, 2017 at 18:35
• I am not suggesting there is a sampling error. I am looking for an estimate of the standard deviation based on a large number of recounts. In science, which is my background, error refers to the standard deviation on a measurement.
– bon
Jan 14, 2017 at 18:38
• @KDog - No you couldn't. The error cannot adequately be determined based on just two observations. That was covered in my answer already. Unless you are assuming that the audit results do not suffer from measurement error, which is impossible. Jan 14, 2017 at 21:42
• There could be an experiment, in which the same group of ballots was repeatedly counted without an actual election being held. But the number of ballots needed for a reliable estimate of measuring error would be quite high (I would guess > 10000), so it's possible no one has ever done this. Jun 19, 2017 at 10:33

I think that given the recounts that have occurred historically, such an analysis is possible. But I don't know if it's actually been done.

Here's a very quick and simplistic analysis using two historical examples.

In the 2004 Washington governor election, there was a machine recount and a manual recount. Each recount changed each of the leading candidates' vote shares by about 0.003%.

Gregoire: 48.8666% → 48.8702% (+0.0036%) → 48.8730% (+0.0028%). Rossi: 48.8759% → 48.8717% (-0.0042%) → 48.8685% (-0.0032%).

In the 2008 Minnesota senator election, there was one recount. The average (absolute) change was about 0.007%.

Coleman: 41.988% → 41.984% (-0.004%). Franken: 41.981% → 41.991% (+0.01%).

So based on these very limited data, we might say that the measurement error is typically between 1 in 100,000 and 1 in 10,000.

There are plenty more data from recounts throughout history. Also, we can look at county-level data. Hopefully some academic will take on this task and do a more proper analysis.

P.S. Another very useful example would be Florida 2000. There was subsequently an academic project to get a better count of the vote (Florida Ballots Project), so you can compare the counts from Nov and Dec of 2000 to the count from the Project.

Something like this was asked in a statistics related group. First, in an election, "statistically significant" doesn't matter. A majority is a majority. A majority of one vote is a majority.

A different question: In the UK, about 51.9 percent of voters voted to leave the EU. If you picked about 30,000 voters absolutely randomly, the chance that less than 50% of these 30,000 would vote to leave would be less in a billion.

• I don't think you understand the question. When the votes are counted there is human error. If you recounted all the votes ten times you would get different numbers. What I'm interested in is if anyone has done any analysis on past recounts to estimate the standard deviation on these numbers and hence give an estimate of the error on the total number of votes.
– bon
Jun 27, 2016 at 7:53