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December 15, 2004

Measurement Error...in the Count

A quick break from exit polls...

Alert JW, a resident of Washington State, asks this interesting question highly relevant to the ongoing recount in that state's race for Governor:

Can a vote that is only "decided" by 42 votes out of 2,800,000 ever really be accurate? We're going into our 2nd recount, and I bet that the various totals given by each recount approximate the variation that exists in sampling polls if your sampling size was 2.8 million. Does anyone ever talk about this thing?

Actually, some have. When the presidential recount in Florida came down to a margin of a few hundred votes either way, Johns Hopkins University President William R. Brody penned a Washington Post OP-ED piece on this very point:

But before we rush to conclude that a recount will resolve any closely contested election, consider this simple fact: A plurality of 300 votes out of nearly 6 million votes cast constitutes a margin of only 1 in 20,000. If we wish to recount the votes to determine whether the number 300 is indeed correct, we must be accurate in the recount process to much better than 0.005 percent.

Put another way, if you or I were asked to recount votes in one of the Florida precincts and were given a stack of 20,000 votes to count, we would have to perform the recount with zero errors! Just one error in the 20,000 ballots would be equivalent to the 300-vote margin that Gov. George W. Bush finished with in the recount.

I don't know about others, but I can assure you that there is no way I could count 5,000 ballots, let alone 20,000, and maintain 100 percent accuracy. Simply distract me for one second while I'm counting and I could easily make a mistake.

We, the American people - and in this case, most especially the media - have tacitly assumed that voting is an intrinsically accurate process. But even in the absence of ballot tampering, no voting process can be expected to be 100 percent error free...

All of which raises an important question. What is the intrinsic accuracy of the voting process, of the voting machines and tallying methods? I suspect that most people would be happy to learn that vote counting was accurate to 0.05 percent. But in 6 million votes, that error rate would translate into a 3,000-vote margin of error - clearly not accurate enough for this election. If we knew the error rate, we could perhaps put into a statute the requirement for a runoff election whenever the margin was less than the voting error rate.

Now consider this issue in terms of surveys. We have been discussing sampling error in recent posts, the random variation that comes from drawing a random sample rather than interviewing the entire population. In tabulating the vote there is no sample, hence no sampling error, yet small tabulation errors still occur. Brody wrote about errors four years ago; such errors certainly remained prevalent this year. In surveys, these inevitable tabulation errors are usually random and offsetting. Absent strong evidence to the contrary, I assume most such errors in the vote count were similarly random.

[Because someone will ask: Yes, I have seen claims that "100% of the reports of improper vote tabulation" benefited George Bush, but so far at least, I have not seen systematic evidence beyond the anecdotal. If you know of any such effort, or any effort to debunk these claims, please post a comment.]

Another source of error suggested in the Florida recount, but not touched on by Brody was a broader conception of what survey researchers call "measurement error." We know that four years ago, many Florida voters went to the polls intending to cast vote for one candidate, but did not ultimately have their choice recorded as intended because of confusing "butterfly" ballots and or improperly punched chads that voided their ballots. Obviously, there was considerable debate -- legal and political -- over whether a recount could have corrected some of those errors. Whatever side of that debate you were on, it is clear that there was some fuzziness in the count then and now.

If measurement error can be a factor in something as seemingly straightforward as balloting for president, imagine how important it can be on more complex issue questions that frequently show up on opinion polls. Ideally, a survey researcher will try to minimize measurement error by "pre-testing" questions - do they measure the things we want them to? The Mystery Pollster assumes the issue of potential "measurement error" will come up again and again as we broaden our focus a bit in 2005.

Related Entries - Measurement Issues

Posted by Mark Blumenthal on December 15, 2004 at 04:23 PM in Measurement Issues | Permalink


I've been a divisional returning officer in an Australian election. A DRO has to conduct the election and then count the votes in a legislative district with a population of around 100 000. You're not allowed errors and you don't get paid until you can reconcile everything from the number of ballots issued to those cast and counted.

The example of counting 20 000 votes in your head is ridiculous.

You sort the ballots into bundles of 100. You double check for purity and accuracy. If your final count does not equal the total number of ballots you check again to find out why. You keep separate records of rejected ballots and the reasons for rejection. You do all this in the presence of scrutineers from the parties and any wandering citizens who wish to observe. You are open to the media at all times. You report to the electoral commissioner who is subject to judicial review.

Bankers used to count cash in the same manner. It's not a matter of amateur counting in your head, it's a matter of ensuring that systems get followed and numbers add up. Admittedly Australia relies on a professional electoral commission to count elections, but perhaps the US needs to consider that.

Posted by: Alan | Dec 15, 2004 10:20:11 PM


I'll second that idea of an election commission, or at least let's have some realistic discussion of very real problems in the collection of the vote that doesn't get shuffled off the table because the election's over. When you have a state official in charge of voting also sitting as the chairman of the states re-election campaign for his parties candidate, even if they're honest you have to say, 'hmmm. That's probably not a good idea.' When it's a crucial electoral state, as in the case of Ohio and in the last election, Florida, even in the absence of malfeasance it questions the legitimacy of the process.
Or to put it another way: that's nuts, no matter what party is in charge.

And clearly there needs to be standardization and validation of the process of collecting and tabulating the vote, and that process should be transparent. Ideally it should not be under the control of local officials but practically that may not be possible, hence the need for transparency and verification. Oregon's recent experiment with vote by mail might be a good jumping off point for the discussion, but clearly the discussion needs to take place.

Posted by: dave_d | Dec 16, 2004 8:36:59 AM

I disagree with the assertion you need such accuracy in counting votes. Although I do agree it is certainly possible to attain such a high accuracy.
Because as long as your errors are non-systemic, with such a large sample as 2.8 million votes...
the random errors will cancel reducing the margin or error.

Posted by: Brian Patt | Dec 16, 2004 12:03:23 PM

Mandating a run-off when the margin is below a set percentage will solve nothing- the initial vote winner will demand recounts when the first counts show the margin to be too little, and the loser will demand recounts when the margin is just a little beyond the mandatory margin. Same problem for different reasons.

Posted by: Yancey Ward | Dec 16, 2004 2:23:06 PM

For what it's worth: My intent in excerpting Brody's passage was not to endorse every word of his piece (I don't) but to note that the system has some small and (hopefully) random intrinsic error.

While the move to electronic voting may lessen vote spoilage, it obviously creates the potential for other mistakes (or worse). The lack of an audit trail in some electronic voting systems is something that should trouble us all, regardless of the accuracy of this year's count.

I appreciate that there are systems that will minimize human error, and that Brody's example may be a bit exaggerated. Still, anyone who has dealt with election clerks or poll workers in the US knows that human error in our process is inevitable. I agree that our system requires some sort of recount or audit procedure in exceptionally close elections to assure faith in the process.

Posted by: Mark Blumenthal | Dec 16, 2004 4:38:03 PM

There's the famous remark by Jimmy Carter that his centre would not monitor a US election because their pre-conditions include an independent, neutral and professional election management body. I suspect as much of the US problem flows from having non-professional electoral officers as comes from having partisan electoral officers.

The biggest reason for an independent electoral commission is that you get professional systems in place and you can hold career officers to a much higher and uniform standard, that fragmented amateur officials just cannot achieve.

For the record, the Australian state of Victoria experimented with postal ballots and abandoned the system because of the possibility of significant fraud with stolen and intercepted ballots. The 1999 federal constitutional convention was elected by postal ballot and that exercise was widely regarded as less than satisfactory and has not been used since.

Posted by: Alan | Dec 16, 2004 11:37:27 PM

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