Did Mahmoud Ahmadinejad Steal the 2009 Iran Election?

Complaint: The Announcement of Ahmadinejad’s Victory Was Suspiciously Premature

Mousavi complained that the Interior Ministry declared Ahmadinejad’s victory prematurely in the early morning after the election, long before the estimated 40 million ballots could have been counted. Iran’s official news agency had jumped the gun even more, announcing Ahmadinejad’s victory on election night after only 5 million votes had been reported, showing Ahmadinejad with 69% of the vote.

According to Mousavi, these premature announcements proved the government had decided long ago that Ahmadinejad would be the “winner” no matter what the ballots might show. Mousavi found this especially irksome because, he said, an official had informed him on election night that he had won and should prepare himself accordingly. This may have been what persuaded Mousavi to announce his own “victory” on election night, before either of the government announcements. Mousavi’s premature announcement predictably induced his ecstatic supporters to take to the streets in celebration, though their enthusiasm was soon dampened by the conflicting pre-announcement of Ahmadinejad’s victory issued by Iran’s official news agency.

This charge almost certainly has no merit. Most obvious, any election-riggers worth their salt would wait for the “cover” of a completed vote count before announcing that their preferred candidate had prevailed. Nor would they pointlessly ruffle the feathers of the pre-determined loser by misleading him to believe he had won. Most important, the timing of these announcements provided no support for Mousavi’s key argument: that the premature announcement was proof of fraud because 40 million ballots could not have been counted so quickly. The Interior Ministry’s job was not to count ballots, but rather to tabulate the field counts reported by 45,692 polling stations, a far less time-consuming task. The field counts certainly could have been completed well before the morning announcement, and routinely had been in previous elections. After all, election-evening field counts were conducted simultaneously at 45,692 polling stations across Iran, in nearly all cases under the watchful eyes of opposition observers.

Complaint: Ongoing Protests and Brutal Repression Prove That Most Iranians Support Opposition

Although the opposition’s pre-election rallies were carried out with little interference, police and militia cracked down very hard on post-election protesters, reportedly injuring many of them and killing several. The opposition described this response as both a brutal suppression of human rights and a tacit admission that the election had been stolen from Mousavi. The government claimed its harsh reaction was justified because the marchers had become violent after the election, setting fire to buildings and vehicles, throwing rocks, and beating police and militiamen. In short, protesters considered themselves the vanguard of true democracy, while the government considered them violent anti-democrats who could not accept that their candidate had lost a fair election.

Mousavi’s supporters held several large protest rallies immediately after the election, and smaller but still sizable rallies during the last half of 2009. The December 21 funeral of Ayatollah Hossein Ali Montazeri, a highly respected cleric and often fierce critic of the government, served as a rallying point for the opposition. The year closed with a multi-day protest held during the Muslim holiday of Ashura, culminating with a large opposition rally on December 27, which was followed by a larger pro-government demonstration three days later. As had occurred before the election, Western press coverage focused narrowly on the opposition rally. According to a guest op-ed published a week later in the New York Times, opposition sources had estimated the December 27 protest crowd in the “tens of thousands” and other sources had estimated “2,000 to 4,000.” A third source, said to be an opponent of Ahmadinejad, had estimated the crowd at the December 30 pro-government rally at 1,000,000 people. The last of these estimates may have surprised readers, since most Western news accounts had reported a much smaller pro-government crowd. The most extreme example had appeared in a long article by Michael Slackman published by the New York Times on January 1, 2010. In an otherwise detailed account of the preceding five days’ events, Mr. Slackman estimated the December 27 protest crowd at “tens of thousands,” but did not even mention that a pro-government rally had occurred.

Nor did the Western press always report accurately the views of Iranians about the election and the protests that followed. Many writers relied heavily on Twitter feeds and similar input from computer-savvy Iranians. For example, Marc Ambinder, writing in The Atlantic, cautioned his readers not to “equate the size of one’s twitter follower universe with authority,” but promptly ignored his own advice: “I’d judge [this Twitter source] as reliable because none of the other twitterers are arguing with its conclusion, and there is some independent corroboration for some of what it has to say.” Among other gory events, Ambinder’s Twitter source reported “militia with ax, chopping ppl like meat,” after which “they pull the dead into trucks – like factory.” Other reports were less upsetting: “All shops was closed – nowhere to go,” and “we lost internet.” Though Ambinder did not mention which of these Twitter tweets had been corroborated, his readers may have feared the worst.

Other data suggest that many Iranians held different views of the election and the post-election protests. According to a poll taken shortly after the election, 76 percent of Iranian voters, including most of those who said they who had voted for Mousavi, believed that the election had been fair. This percentage rose to 83% in a second poll taken approximately two months later. Many Iranians felt that opposition protesters were deliberately provocative at times, and that police and militia reactions were not excessive. For example, although most Western news reports criticized the Iranian government for its harsh response to the December 27 protest during Ashura, an important Muslim holiday, many Iranians instead blamed the opposition for having scheduled a protest rally during that important Muslim holiday. It was predictable, many Iranians felt, that the burning of police vehicles and chants of “Death to the Leader” would lead to violence. Contrary to the expectations of some opposition leaders, it may be that few neutral Iranians interpreted the government’s harsh response as an effort to hide its own illegitimacy.

Complaint: Shutdown of Electronic Communications Prevented Opposition from Monitoring Election

Though reports differ greatly on the extent and duration, both sides acknowledge that various forms of electronic communication were shut down by the Iranian government on election day. The government attributed this to technical problems. Opposition candidates and their supporters argued, more persuasively, that the shut-down was intended to make it more difficult for them to coordinate election-day activities.

Whatever the reason, it is not clear that the communications shut-down had any material effect on election day. By law, campaigning had ended two days earlier. At the least, land-line telephones and all modes of transportation were operating normally throughout the day. Mousavi did not suggest that the shut-down had prevented any of his observers from reaching their polling stations, or from performing their duties while they were there. Get-out-the-vote efforts may have been hampered to some extent, but all candidates were probably affected much the same. In fact, since get-out-the-vote efforts usually focus on less-motivated voters, the communications shut-down may have harmed Ahmadinejad more than Mousavi.

Complaint: Statistical Analysis of Vote Counts Shows Fraud Occurred

Though several statistical challenges to the election result have been discussed above, some esoteric “digit frequency” analyses deserve a closer look. It happens that the digits 1 through 9 do not appear with equal frequency as the first significant digit in numbers found in many (not all) real-life data sets. Instead, the lower the digit, the more likely it will appear as the first significant digit in such a number. The likely frequency of each digit can be calculated under what is known as Benford’s Law. If human tampering is suspected, sometimes this can be detected by comparing the first-digit frequency of 1 through 9 in the data with the frequency one would expect under Benford’s Law. Benford’s Law analysis can also ferret out computer-generated numbers. For example, under Benford’s Law, the digit 1 would be expected to appear roughly 30% of the time as the first significant digit, far more often than it would appear in a randomly generated batch of numbers.

Several statisticians analyzed voting data from the 2009 Iran election under Benford’s Law and similar “digit frequency” statistical models. Based on his “first digit” Benford’s Law analysis of county-level data, Professor Boudewijn Roukema concluded that the number of vote counts starting with 7 for Karroubi (who received less than 1% of the vote) was large enough to indicate that fraud had occurred. Ahmadinejad’s county-level totals also struck Roukema as suspicious – too many 2’s, not enough 1’s. Professor Walter Mebane pointed out, however, that Benford’s Law has not proved useful in many elections when one analyzes the first significant digit of a vote-count number. It nonetheless is useful, Dr. Mebane believes, if one analyzes the second significant digit. He did so, analyzing both district-level data and ballot-box level data. Though he found nothing suspicious in the district-level data, Dr. Mebane concluded, with “well beyond 99%” certainty, that the ballot-box counts for Ahmadinejad, Karroubi and Rezai showed suspicious distortions; Mousavi’s did not. Professor Mebane believed that fraudulent vote counting was the most likely explanation for the suspicious Ahmadinejad results, though he stressed the need for additional information and further investigation before drawing any firm conclusions.

Less restrained than Professor Mebane were two other statisticians, Bernd Beber and Alexandra Scacco – then graduate students at Columbia University, now professors at New York University. They analyzed province-level data and focused on the final digit, and the final two digits, of each vote-count number. Their conclusion, prominently displayed on the Washington Post’s op-ed page: “a bet that the numbers are clean is a one in two-hundred long shot.”

It is not difficult to invalidate the analyses of “digit frequency” statisticians who found Iran’s 2009 election results to be suspicious, starting with Beber/Scacco. Essentially as they explain, if a person is asked to write down, say, 100 freely chosen five-digit numbers, certain combinations of the final two digits in those numbers are more likely than others – for “human” reasons that have nothing to do with statistical probability. For example, 23 is more likely than either 64 or 17 because “people have trouble generating non-adjacent digits.” Therefore, if pairs of “adjacent digits” appear substantially more frequently than is statistically likely (29%), we may suspect that a human being has chosen the digit pairs. Similarly, if a particular single digit (0 through 9) appears as the final digit of a number substantially more or less frequently than 10% of the time, we may suspect that a human being has chosen the digit. Beber and Scacco looked at 116 numbers, vote totals for each of the 4 candidates in 29 provinces. They found that “adjacent digit” pairs appeared suspiciously often (38%), that 7 appeared suspiciously often as the final digit (17%), and that 5 appeared suspiciously infrequently (4%). They concluded, with 99.5% certainty, that the vote counts reported by Iran’s Interior Ministry had been “manipulated.”

But not one of those 116 numbers could possibly have had any “human” input. Each province-level total, after all, is merely the sum of all ballot-box totals in the province. Ballot-box totals are the basic elements of all higher-level totals: district, county, province, and nation. If the province-level total does not match the sum of its ballot-box totals, we indeed will suspect that “manipulation” occurred, but we will not need a statistician to tell us that. Simple arithmetic will do. If we instead assume that the would-be “manipulator” will be careful enough to make sure that each province-level total matches the sum of the province’s ballot-box totals, he will have no choice when he writes down the province-level total. If the hundreds of ballot-box totals add up to a number that ends in 64 or 17, or some other unappealing pair of “non-adjacent digits,” then that is what he must write down, however strong may be his subconscious urge to write down 23 or some other pleasing pair of “adjacent digits.” The same is true for any other “aggregated” vote total, such as the county-level totals analyzed by Dr. Roukema and the district-level totals analyzed by Dr. Mebane.

Whether or not Beber/Scacco had recognized this fatal flaw, their 99.5% certainty of fraud plummeted sharply once they had reviewed county-level data: “After we wrote our op-ed using the province-level data, we’ve now also done some preliminary tests with the county-level data. In the latter dataset, the last digits don’t appear fraudulent.” They also acknowledged that each province-level total matched the sum of its county-level totals, which left them no apparent basis for their earlier op-ed conclusion.

Despite this setback, and though they acknowledged that “this is just speculation,” Beber and Scacco laid out a possible scenario that illuminates a slight overstatement two paragraphs above. The analysis there presumes that one starts with lower-level numbers (for example, county-level), aggregates them into higher-level numbers (province-level), and then statistically tests the higher-level numbers. It concludes that the higher-level numbers cannot have been manipulated because they are aggregated numbers. But what if one were to start by manipulating the top-level numbers and then work backwards to “harmonize” their lower-level components? Perhaps, Beber and Scacco speculate, Ahmadinejad’s Interior Ministry henchmen decided on election night to “adjust” his province-level numbers. For one reason or another, they decided to give him five million votes more than he needed to avoid a run-off election, making the number-adjusters’ task that much more daunting. This large adjustment would need to be spread over many provinces to minimize the risk of detection. For the same reason, each province’s adjustments would need to be spread over many counties. Most of that county-level burden, though, would be borne by the first and second digits of vote-count numbers, where adjustments would have the greatest quantitative impact. The final two digits – the only digits that Beber and Scacco would look at – would need to be adjusted for only one county per province, just to fine-tune the sum, and a single-county adjustment was not detectable under the Beber/Scacco model.

The Interior Ministry’s manipulators managed to stay under the Beber/Scacco radar when they adjusted county-level numbers. It appears they had more than a passing familiarity with the statistical model that Beber and Scacco would employ to check their work. Whether haste or hubris was to blame, however, the manipulators had failed to apply their impressive knowledge when adjusting the province-level numbers, and so Beber and Scacco had uncovered their plot before they even turned to the county-level adjustments. In addition, though Beber and Scacco do not mention this, the manipulators’ number-doctoring chores had just begun. Once county-level numbers have been adjusted to harmonize them with doctored province-level numbers, district-level numbers must then be adjusted to harmonize them with the now-doctored county-level numbers, and then thousands of ballot-box numbers, in turn, must be adjusted to harmonize them with the new district-level numbers. This would require a great deal more work, and pose a far greater risk of detection by Beber and Scacco or a sharp-eyed Benford’s Law analyst. The prospects of this “working backwards” scenario may be brighter than they appear here, but Beber and Scacco do not explain why that is so.

But what about Professor Mebane’s “second digit” analysis of ballot-box data under Benford’s Law? He might argue that ballot-box counts reflect no aggregation that would eliminate the possibility of human tampering. Dr. Mebane concluded that divergences from Benford’s Law were “insignificant” for Mousavi but “highly significant” for Ahmadinejad, Karroubi and Rezai. Other causes might explain the Karroubi and Rezai results, but he saw only one possible explanation for Ahmadinejad’s suspicious results: fraudulent vote counts.

As explained above, a regional vote count cannot possibly have been “manipulated” if it matches the sum of its underlying ballot-box totals. For essentially the same reason, if we determine independently that ballots in a box were properly cast and counted, Benford’s Law analysis can prove no more about that ballot-box count – nor about any data set that includes it – than it can prove about a regional vote count. Just as the latter number is an aggregate of ballot-box counts, a valid ballot-box count is merely the written-down sum of votes in the box, and so the ballot-box count cannot reflect human tampering. Dr. Mebane’s ballot-box level tests cannot be considered meaningful, therefore, so long as his data include ballot-box counts whose validity has been independently established. If, as suggested above, we treat a ballot-box count as valid if a Mousavi observer approved it in writing (an “observed” ballot box), and conservatively classify all other ballot boxes as “unobserved,” it might be useful for Dr. Mebane to conduct “second digit” Benford’s Law tests exclusively on the “unobserved” ballot boxes. If the result appears suspicious, a more thorough investigation for fraud can be conducted, using non-statistical methods as Dr. Mebane himself recommends in such circumstances.

Professor Mebane found another significant correlation that does not involve Benford’s Law analysis – a ballot-box-level correlation between (1) low invalid-ballot percentages; and (2) high Ahmadinejad vote percentages. Although other commentators offer benign explanations for this correlation, some merit initially appears in Dr. Mebane’s more skeptical view. First, if the vote-counters prefer Ahmadinejad and are not watched carefully enough by Mousavi’s observer, they might count an ambiguous ballot, or even a plainly invalid ballot, as a vote for Ahmadinejad. This will have the dual effect of increasing Ahmadinejad’s percentage and decreasing the invalid vote percentage, resulting in precisely the correlation Dr. Mebane detected. Second, an unusually low invalid-ballot percentage might mean that ballots were added for Ahmadinejad. Ballot-box stuffers rarely recognize the need to add some invalid ballots as well, and so the invalid-vote percentage drops as fraudulent but “valid” ballots for the favored candidate are stuffed into the box.

The response should be familiar: vote counters indeed were watched closely by Mousavi representatives, or so they represented by witnessing the field counts and not disputing the reported results. The miscounting of invalid ballots or the addition of ballots for Ahmadinejad, especially on the grand scale necessary to make a difference in the 2009 election, almost certainly would have been detected. Disputes over questionable ballots are often the most hotly contested matters in the vote validation and count process, an otherwise dull chore. It is unlikely that a Mousavi observer will have approved a vote count if he believed that more than a few, if any, invalid ballots had been counted as Ahmadinejad votes, or if he suspected that the ballot box had been stuffed while he was not watching.

Conclusion

No credible evidence published so far indicates that Ahmadinejad stole Iran’s 2009 presidential election – or, for that matter, that any fraud at all occurred. The second point is important because many commentators have grudgingly accepted Ahmadinejad’s legitimacy only because his margin was large enough that they believe he would have won even without cheating. Nearly as telling, there appears to have been no serious effort by Mousavi or his supporters to find such evidence. Shortly after the election, Mousavi claimed in his newspaper (Kaleme) that 10 million people had voted without showing proper identification, but his complaint to the Guardian Council mentioned only 31 such voters. Widespread ballot-box stuffing was alleged, but not a single stuffed ballot box has been identified. Wholesale buying and selling of votes was alleged, but Mousavi has identified only four instances, in each case without any evidence. Thousands or millions of Mousavi votes were said to have been thrown away, replaced by thousands or millions of Ahmadinejad votes, but no one has identified any of the perpetrators, nor mentioned exactly where or how this was accomplished. Vote counts from the field, approved by tens of thousands of Mousavi’s observers, were said to have been altered by the Interior Ministry in Tehran, but no one has identified a single ballot box ­where this occurred – even though the data have long been available to compare the counts for all 45,692 ballot boxes. The silence of Mousavi’s polling station observers is especially deafening. Most or all of them may believe that electoral fraud occurred all over Iran, but apparently each is equally adamant that it did not occur where he spent Election Day.

Nor have independent critics maintained their initial enthusiasm. The Chatham House Preliminary Analysis never advanced beyond its self-described “preliminary” stage, despite the author’s own suggestion that his brief analysis “be followed up should the fully disaggregated ‘by polling station’ data be released during the ongoing dispute.” Precisely that data was released just days later (see note 1), but no “follow up” has appeared. The response of nearly all pro-Mousavi analysts to the published ballot-box data has been largely the same: silence. Statisticians such as Roukema, Beber and Scacco appear to have ignored it entirely. Even the few who have examined ballot-box-level data – Professor Mebane, for example – have overlooked or ignored its real significance. For the first time ever in an Iranian presidential election, it was a simple matter to find evidence of vote-count fraud: just compare the Interior Ministry count with the field count approved by a Mousavi observer, for any ballot box or for all of them. It is fair to ask why no one has done this, or why they have not published their findings if they have.

Despite the absence of evidence – or perhaps because of it – Mousavi’s demand has never changed: Don’t investigate the election; just toss it out and do it over. One wonders how Americans would have reacted if Al Gore had demanded this in 2000. Mousavi has never explained what would happen if a second election were held and it yielded the same result. Would he demand another do-over, and then another, until Iran’s voters get it right? Even his most ardent supporters eventually would insist on evidence. If eventually, why not now? It is not fair to the 24 million Iranians who appear to have voted for Ahmadinejad – nor is it democratic – for a government to “compromise” with a defeated candidate by nullifying an election without a sound basis for doing so. The loser has a right to complain about an unfair election, but the winner, and those who voted for him, have an equal right to insist that a valid election be respected. One side will always be disappointed with an election result – but that is democracy, not fraud. Fraud requires evidence, not merely surprise, disappointment and suspicion.

All of this matters outside Iran as well. One suspects that Western leaders acknowledge Ahmadinejad’s legitimacy when they talk privately with their foreign counterparts, but many of them posture in public. Even those officials who have been comparatively restrained in their public statements on the election (US Secretary of State Hillary Clinton, for example) welcome support from election-doubters for confrontational stances they take toward Iran on other grounds. Most Western media outlets routinely refer to the election as tainted, and many writers insist that policy toward Iran must reflect this. Those who disagree are often described as regime apologists, or naive at best. But they are merely accepting the election result. It is time others did too.