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The Ayatollah’s Flawed Logic

I don’t know how many people caught this expression of logic from Ayatollah Ali Khamenei in his call for an end to the protests over the electoral outcome in Iran. As reported by the BBC:

Responding to allegations of electoral fraud, the ayatollah insisted the Islamic Republic would not cheat.

“There is 11 million votes difference,” the ayatollah said. “How one can rig 11 million votes?”

This particular argument is not unique to the Ayatollah. It has also been used by some Western observers such as Flynt Leverett (emphasis mine):

SPIEGEL ONLINE: Still many people, including in Washington, have expressed skepticism as to the validity of the results.

Leverett: I am a little surprised by the margin, too. But that makes me more comfortable about the overall validity of the election. Look at the irregularities Mousavi is citing now: that they ran out of ballot paper in some polling precincts, that they did not keep some polls open long enough. There is no way such things could change the overall outcome which is clearly in favor of Ahmadinejad. If you compare this to the flaws of the presidential election in Florida in 2000, it seems very insignificant.

Leverett and Ayatollah are arguing from an ironically Western conception of how to rig an election. In the United States, it is actually rather difficult to steal an election: because of our federalist system, elections are monitored and voting totals are reported by hundreds or thousands of individual officials at the state, county, and precinct levels. There is therefore a rather substantial marginal cost to stealing additional votes: you have to recruit some number of additional people into the conspiracy, and hope they don’t rat you out or leave some kind of paper trail that makes obvious your intention. It is probably not that difficult to find a few corrupt (but competent) stooges who will help you out, but for each additional vote that you want to steal, you have to go lower down the food pyramid, soliciting the help of people who are less loyal and might undermine your plan.

But this is simply not the case in Iran. All votes are counted are reported by the Interior Ministry. There is no other source of information. There are no election monitors. Nor does the fraud alleged involve any sort of physical process (e.g. stuffing ballot boxes). It is simply a matter of changing numbers on a spreadsheet. Under these conditions, it is essentially no more difficult to steal a thousand votes than one, a million than a thousand, or 11 million than one million.

The only constraints, rather, are perceptual: certain vote totals might be more or less likely to trigger protests and unrest. It is probably easy to identify those voting margins that are most likely to trigger unrest: one would be to claim to have won the election (or secured enough votes to avoid a run-off) by exactly one vote; the other would be to claim to have won the election with 100 percent of the vote. In the former case, you would almost certainly wind up being subject to a recount, and any one report of irregularities could undermine your claim. In the latter, your claim would a laughable on its face, and every single Iranian who had voted against you would know that his vote had been stolen and would take to the streets.

It is less clear the margin of victory that minimizes the risk of unrest. But one can posit a curve that looks something like this:

I’d imagine there’s a fairly broad sweet spot somewhere between about 55 percent of the vote and 75. Totals below 55 percent might trigger piecemeal scrutiny of irregularities and/or otherwise embolden your opponents, either of which could ultimately cost you the “victory”. A claim to having won more than 75 percent of the vote would stretch credibility in an ethnically diverse country where there is clearly a lot of political disagreement; you’d have gotten too greedy. Ahmadinejad’s claim to have won 63 percent of the vote falls somewhere in this sweet spot. That doesn’t mean he stole the election — but it also doesn’t mean that he didn’t.

Nate Silver founded and was the editor in chief of FiveThirtyEight.