Numbers Are Bad Liars

After Mahmoud Ahmadinejad was declared the winner of Iran’s June 12 presidential election, protesters have been crying fraud. In a Washington Post op-ed, Bernd Beber and Alexandra Scacco claim that the truth lies in the digits of the vote count. Humans are bad at making up fraudulent numbers, they write, and the fact that the vote counts for the different provinces contain “too many 7’s and not enough 5’s in the last digit” and not enough non-adjacent digits points to made-up numbers. Iran’s election monitors, meanwhile, acknowledged that the number of votes exceeded the number of voters, but deny fraud. [%comments]


And our response is, sadly, tepid. Yes we can.

Eric M. Jones

Brilliant. Now I know how to fix national elections with greater finesse than Republican operative and Rove's IT fixer Mike Connell, who (err,,,) died in an untimely plane crash before he could be subpoened to testify.

Years ago a friend of mine took me to a used car lot where there were scores of used VW beetles. He told me to check the odometer. I saw that it had 76,000 miles more or less. He insisted I check another one. It had about 76,000 miles. And another and another.... They all had about 76,000 miles.

Apparently the mechanic who was ordered to spin back the odometers using his electric drill was sending a plaintive message to honest buyers to avoid the place.

J. Daniel Smith


1) What is to stop people (regimes) in the future from doing this type of analysis *before* releasing (fixing) the numbers?

2) I'll take 1/200 odds in the lottery any day.

3) What happens when you run this analysis against other sets of "random" number such as digits of e, pi, stock prices, etc.?


The easy way to beat this analysis is, of course, to randomly generate every digit after the first one.

So if you want to win by 10,000 votes or more, just write down the "1" and randomize the other four, then subtract that number from the total possible votes.

You can avoid the question of "where did those other three million votes come from?" Unless, of course, you're a dictatorship that doesn't really care if the people know you're screwing around with the vote totals.

Has anyone ever applied this analysis to the Florida 2000 vote counts? It could be the final nail in the coffin for the "Bush stole the vote" nuts.



It's not so simple, so no worries, and I'm thinking the Kennedys or the Chicago mayoral royalty might be a better benchmark to shoot for.

Doctor Gonzo

What is the U.S. response supposed to be? Invasion? Bombing? Sending in our military to install Mousavi?

Iran is a sovereign nation. All we can do is express our desire for the truth to come out (and make our Twitter avatars green, since that will help a lot). We can't do anything more without turning this into a nationalist, Iran vs. U.S. event that certainly won't help progressive voices in Iran.

Whenever people say we should be throwing our weight around when it comes to votes in other countries, I ask them this: if Iran, or Iraq, or China, or Venezuela, or pick-your-country came out forcefully against the fraud in the 2000 elections, would that make you less likely to support our country and more likely to think that they were right? Or would you view it as absurd meddling from a country that should mind its own business? Yeah, I thought so.


Cirby, there are plenty of things that went wrong procedurally which a statistical analysis wouldn't catch. For example, it's a problem when the person who makes the final judgement for the electoral votes of the state also actively campaigned for one of the candidates.


Hey, if it's good enough for Florida, it's good enough for Iran.


numbers from the last posts


i think the harvard contest people really care more about themselves and reunions


please update that comment count to 3,8, 21 in just the time it took me to type that.

wow, and i bet those people don't even mneed the prize. It's amazing what people will do for free.

Mike Kriskey

Dr. Gonzo--

I don't recall Al Gore's supporters asking the government of Iran to lend moral support to their candidate. At least not publicly.

Fritz Mills

Not to mention the fact that they were seemingly able to count 40 million ballots by hand, and complete the count and announce the results only 2 hours after the polls closed. And, despite the fact that Iranian law calls for a three day period to review and certify the results, that process was accomplished in less than a day.



The reality is that while it is suspect there may be fraud; there is no proof. The claim by the IRGC that having over 100% voter turnout in some places is common historically because of the way the election system works(You can vote anywhere in the country, not just in your precinct) does not seem to be disputed by any qualified analyst or academia. Only by twitterers and sensationalists.

Even with from all accounts if there is fraud, Ahmadinejad still won. There is simply not ENOUGH fraud to cover a 30%+ vote gap.


Doctor Gonzo:
What is the U.S. response supposed to be? Invasion? Bombing? Sending in our military to install Mousavi?

How about something stronger than "I'm concerned?" Why not "we support freedom and democracy in Iran, and dislike totalitarianism?" There are more responses than "do nothing" and "kill everyone." Pretty much every other democracy and republic on the planet has come out in favor of fair elections and democracy in Iran, why not our President? How about a "hey, guys, your election was embarrassingly fraudulent, how about running a fair one for a change?" If President Obama can't manage to point out that they're doing this, how well-run do you think his negotiations will be over the nuclear issue?

...except that if there WERE shenanigans in Florida in 2000 (of the type usually claimed), statistical analysis should be able to find the changes quite easily. So far, in four major recounts and many other studies, nobody's found anything to support your view - in fact, they found quite the opposite. And if you have problems with one person being in charge of the vote resolution, how do you feel about the fact that Democrats were running 11 of the 13 counties that had voting issues? One could make a case that the Democrats were doing the cheating and just screwed up the process.

Statistically, that makes a lot more sense.


Kory Karr

Cirby said:

Why not “we support freedom and democracy in Iran, and dislike totalitarianism?”

Well, because that would be a blatant lie, evident to anyone who cared to look at the facts. Obama even eluded to that in this quote; "Now, it's not productive, given the history of the U.S.-Iranian relations, to be seen as meddling"

History and current events show that we're much more concerned with having a pro-western leader than we are having a democratically elected leader.


I've been expecting this post for days. It might help to add an "earlier" link to past freakonomics articles.

and if they wanted to cheat they should have started each town with +5000 votes (or even plus 2379) for the guy who is being set up to win and -5000 votes for the guy who is being handicapped. under this approach the statistical tests still hold.

"hacking democracy" an hbo documentary raises some of these issues (although that movie is presented from the Gore side of the 2000 election)


I seem to recall that a similar analysis was done during the Vietnam war, and it found that the reported body counts of dead Viet Cong and NVA soldiers was not random, as it would be under normal circumstances.

The military, concerned that body counts ending in 0 or 5 would look "made up", went overboard and avoided those digits as they picked numbers out of thin air.

Thus, there were plenty of daily body counts ending in, say, 2 or 7 or 9, but very few that were multiples of 5 or 10.

Statisticians discovered this, and the lid was blown off the body count cover-up.


What is the probability that there are 17% of one of the digits in a sample of 116 numbers. Can some mathematician work that out?


There's about a 1.1% chance that one digit in a sample of 116 occurs 20 times (17.2%) or more. The odds double to a 2.2% chance at 19 occurrences (15.5%).

On the other side, there's about a 2.1% chance that one digit in a sample of 116 occurs 5 times (4.3%) or less.

At least that's what I get. It's been a while. Correct me if I'm wrong.


The vote total number for each candidate isn't going to be random. It has to add up to the number of votes cast.

I am proceeding under the assumption that while the total number of votes was fixed (stamps on the citizens voting documents, enrollment sheets at the polls), the distribution was what was manipulated. Since the vote total for each candidate is a subset of the "random" number of votes cast per precinct, wouldn't that throw off the analysis? And if it did, could one instead run the same analysis on the precinct totals to look at the possibility of outright ballot-stuffing, or are we below the "statistically significant" threshold?