Like most Americans, there are few things I would like to see more than Mahmoud Ahmadinejad, Iran's hateful President, to be voted out of office. Elections in thuggish, authoritarian states like Iran need be treated with the utmost skepticism and scrutiny. I can't say I have any real degree of confidence in the official results, which showed Ahmadinejad winning with some 62 percent of the vote.
There is a statistical analysis making the rounds, however, which purports to show overwhelmingly persuasive evidence that the Iranian election was rigged. I do not find this evidence compelling.
Iran's election results were reported by its Interior Ministry in six waves. The first wave covered about one-third of the total vote; there were then two relatively large waves that reported about 20 percent of the vote each, and then three smaller waves that reported the remainder of the vote. What other observers have found is that, over the course of the six waves, there is an extremely strong, linear relationship between the number of votes reported for Ahmadinejad and the number reported for his principal opponent, Mir Hussein Moussavi (who had declared victory before any results were officially announced):
This relationship is superficially very impressive -- an R-squared of .998, which suggests a nearly perfect relationship.
Just how remarkable really is it, however? Rather than deal in abstractions, let's try a more concrete sort of experiment. Suppose that results from last November's election between Barack Obama and John McCain were revealed in this fashion, in six large waves. Suppose moreover that these waves were determined based on the alphabetical ordering of the states:
Wave 1: Results from Alabama-Illinois are reported; this represents about 33% of the total vote.
Wave 2: Results from Indiana-Mississippi (17% of the total vote) are added to the above totals.
Wave 3: Results from Missouri-North Carolina (19%) are added.
Wave 4: Results from North Dakota-Pennsylvania (12%) are added.
Wave 5: Results from Rhode Island-Texas (10%) are added.
Wave 6: Lastly, results from Utah-Wyoming (9%) are added and the counting is complete.
If results were released in this fashion, here is what we would get for the total number of votes for Obama and McCain at each stage:
Now, let's plot these on a graph:
Wow! The correlation is extremely high -- an R-Squared of .9959 -- almost as high as the one we saw for Iran. Does that mean the U.S. election was rigged too?
Of course not. The apparently extremely strong relationship is mostly an artifact of the exceptionally simple fact that as you count more votes, both candidates' totals will tend to increase. In our example, Wave 5 happens to be a very good one for McCain: it contains the results from South Carolina, South Dakota, Tennessee and Texas -- four red states -- plus Rhode Island, which went for Obama but contains a tiny number of votes. And yet, the impact of Wave 5 is barely visible when the results are presented in this fashion.
Likewise, there was more wave-to-wave variation in the Ahmadinejad-Moosavi results than the statistical analysis I cited above seems to imply. Ignoring votes for minor candidates, Ahmadinejad won a high of 70.4 percent of the votes in Wave 1, and a low of 62.3 percent in the votes newly added in Wave 6. By comparison, Obama's share of the newly-added votes in our experiment ranged from 56.4 percent in Wave 3 to 44.7 percent in Wave 4. That's slightly more variance than we saw in the Iranian results but not much.
To be clear, these results certainly do not prove that Iran's election was clean. I have no particular reason to believe the results reported by the Interior Ministry. But I also don't have any particular reason to disbelieve them, at least based on the statistical evidence. If Moosavi truly did have the support of a majority of Iran's citizenry, the best evidence we will have of that is what happens in the streets of Tehran over the next days and weeks.
EDIT: In case this isn't clear, I am not suggesting that any and all statistical analysis purporting to show tampering in Iran's election results will turn out to be fruitless. I am merely suggesting that this particular analysis is dubious; it is not a smoking gun.
To properly analyze Iran's election results is probably something best left to Middle East experts, rather than experts on U.S. electoral politics. Juan Cole, for instance, who certainty does know a thing or two about foreign policy, sees plenty of things that smell fishy to him.
Still, though, would it really be all that hard to rig an election in a way that would be hard for statistical analysis to detect? Suppose that you're Ahmadinejad, and that you become convinced based on the actual vote totals that you're on track to lose by several points. Could you not simply take every tenth vote, or every fifth vote, that came in for Moussavi, and count it for yourself? This would preserve an element of randomness and would make the province-by-province results look reasonably correct relative to one another.
My point, I suppose, is this. Out of all the things you'd need to do to rig an election, coming up with a set of results that managed to avoid easy statistical detection would probably be one of the easier ones. So I'm skeptical that statistical analysis alone is going to turn up evidence of fraud. But I'll be keeping an eye out for other approaches, particularly from those who have a deeper understanding of the Iranian state than I do.
6.13.2009
Statistical Report Purporting to Show Rigged Iranian Election Is Flawed
@ 4:13 PM
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Good analysis.
What about the other obvious question, Nate, something I've been asking all day and a reader writes to Andrew Sullivan:
http://andrewsullivan.theatlantic.com/the_daily_dish/2009/06/the-turnout-and-the-margin.html
This is Nate Silver-bait. But an Iranian-American reader asks a good question. Under what circumstances with a turnout of 85 percent do landslides for incumbents happen, as the regime claims in Iran? Are there any precedents for this in electoral history? One way of tackling the question of fraud is simply probability. How many election results in history have never varied from region to region or from the beginning of the count to the end? Does this result have any serious precedents? Or is it as self-evidently rigged as it increasingly seems?
Although Nate's post is persuasive as far as it goes, it leaves out the 85% turnout.
More importantly, the Interior Ministry results claim that Karroubi, an ethnic Lor, got crushed among his own base, as did Mousavi among the Azeri? What say you to that, Nate? That seems to make the uniformity of the Interior Ministry's results much more suspicious than they otherwise would be...
But your analysis is using an effectively random ordering of results and states. From watching returns come in on a state-by-state basis on election night, it was clear that there was significant variance due to the rate at which urban and rural areas report their vote totals (among other reasons).
Sure it's probably reasonable that after the fact a random subsection of votes will mirror the overall vote proportion. But I'm unconvinced that realtime vote totals on election day exhibit the same behavior.
In addition, the stability of Ahmadinejad's proportion of the vote in areas like the home-region of his opponent(s) -- especially urban centers there -- strikes me as extremely questionable.
But why organize the waves by alphabetical order? That seems to highly randomize them in a way that doesn't necessarily seem to be the case with those election results reported by the Ministry of the Interior. Would the variation be the same if you organized the states, say, geographically rather than alphabetically?
Your regression line is using complete vote counts from the states. You should replicate this using the vote counts at several times during election eve, say at 9pm ET, 10pm, 11pm and so on. This more accurately replicates the counts that were released.
I think nate's point is valid, the problem I see is that to maintain the composite of the electorate and thereby the equivalent ratio one needs a selection mechanism which does that. I find that very improbable because it cuts against the natural kinetics of the election counting system whereby there is variation across regions in reporting and those variations ARE correlated to vote share (cities vs rural etc).
I'm skeptical on this one. The states are entered alphabetically. The first letter of a state's name tells us nothing about how it should vote. You've basically begun to randomly select which data points to include in your sample. This should be an unbiased estimate of the population parameter, which is the actual vote total. Try the same analysis by time zone and see if the pattern holds. We have good reason to believe votes should vary by time zone. Additionally, do it by region. The regional fractionalization in the US doesn't compare to that of Iran. I agree that the first graph doesn't scream "fraud," but until we know the counting procedure that underlies the first graph, we cannot say much more about it. If the votes came in by region, or from urban areas first and then the countryside, I would wager my graduate stipend against an R^2 of .998.
In an election between a candidate well-liked in urban areas and another in rural areas one should rather expect that over time, the pro-urban candidate would at least catch up a little, so that the result plot would look more like a curve than a straight line.
You hardly see that in Western election reports, since the TV stations use projections to compensate this (so the projection can be close to the final result), not raw votes as Iran did.
I'd have to share the same skepticism. Was it a similar time progression (what the Iranian results reveal) on Election night, from when the first states polls closed to the last? If so, then I'd be apt to believe the Iranian results a little more. If not, or if no other recent election's results came in in this fashion, I'd have to argue the time progression of these numbers are way too unrealistic.
Is mixing the results an appropriate model here? When you add Alabama and Illinois, you get a set of votes where the high conservative vote in one state cancels out the high liberal vote in the other.
On the other hand, we've all seen cases - typically in elections at the state level - where results from individual counties that heavily favor one side or the other come in one by one, and the percentages change dramatically.
It's worth asking, therefore, whether the "waves" of results in Iran compiled on such a way that mixed result like the one Nate is portraying would have been likely, or should we have expected something with more variability?
The best way to do this is to:
1) See which provinces reported in each wave in Iran
2) See what the appropriate theoretical support for the candidates would have been in each province
3) Compare that to the reported results
I assume the data simly isn't available to do that work in Iran.
Looking at the US, I believe most fo the first states that reported had McCain up slightly in electoral and popular votes, but that's because they closed the polls the earliest.
How do you explain this, though?
http://tiny.cc/LNyfl
Yes but we have to believe him on this one, because he used the phrase "Statistical Evidence" in the title. Motion to permit only Andy the use of that phrase?
[Deleted and reposted because of a split-infinitive. It would have bothered me all day.]
I agree with the others that Nate's analysis doesn't make sense. He's putting the votes in the US into bins in a random manner. Of course the results are going to show a linear relationship.
But the votes in Iran weren't counted randomly. That's the point they're making.
As others said, do the same analysis by time zone, race, gender, blue/red states, etc. You won't get a linear relationship then.
If you look at the differences instead of the totals, that is, each block of new votes by itself (with the first total counted as the first block), the results are not so impressive. The s.d. of the residuals is 121,000 votes.
It would still be nice to know more about the order in which votes were reported, and comparable fits from other elections.
Under what circumstances with a turnout of 85 percent do landslides for incumbents happen, as the regime claims in Iran?
Under many circumstances, I would imagine.
The last Icelandic presidential election had 85.9% turnout with the incumbent winning in a landslide bigger than that seen in Iran. You think that one was rigged?
"Wave 1: Results from Alabama-Illinois are reported; this represents about 33% of the total vote.
Wave 2: Results from Indiana-Mississippi (17% of the total vote) are added to the above totals.
Wave 3: Results from Missouri-North Carolina (19%) are added.
Wave 4: Results from North Dakota-Pennsylvania (12%) are added.
Wave 5: Results from Rhode Island-Texas (10%) are added.
Wave 6: Lastly, results from Utah-Wyoming (9%) are added and the counting is complete."
Right, but, what are the chances of all of that happening? Incredibly low. Oddly shoddy analysis here Nate.
Nate, What you have done more or less here is estimate the lower bound on the wave reporting variance. ANd you did this by homogenizing the sampling (via using alphabetical reporting rather than temporal). If you had resolved the waves temporally one would expect a significant bulge in the middle as the midwest reported then the left coast later.
So an important question is what determined the composition of the waves. Random or unbiased sampling or reporting of inhomogeneous provinces.
Since it's presumably unlikely that the reporting was homogeneous, the constant variance it troubling.
What you should do is compute an upper bound by summarizing the mccain/obama race in 6 waves but use two orderings 1) temporal 2) sorted by the ratio of mcain/obama to give the maximum possible variance.
Scratch my last comment - turnout was only 63% in that election (I misread the Wikipedia article). But the Icelandic presidential election of 1988 had 72.4% turnout and an incumbent victory by 95%.
re: Haukur:
Given the large population discrepancy between Iceland (320,000) and Iran (70.5 million), in addition to Iran being a multi-ethnic country compared to Iceland, which is largely ethnically uniform, I'm not sure how representative the analogy would be. If the same can be found in a country like the US or Indonesia or India, large multi-ethnic countries, then it'd be more convincing.
I'm sitting in my grandparents' house in Tehran right now and I'm hearing mini-explosions, there's helicopters flying around, it smells like smoke, and it took fifteen minutes for this website to load because they've slowed down the internet so much here. On top of that they've basically blocked parts of Iran from the international phone network so I can't even call my mother. 80% of the Iranian people did not enthusiastically turn out in order to re-elect someone who has ruined this country both economically and culturally. The Iranian people know that this election was rigged. How could it have been possible for Mousavi to lose Tabriz when he is from Iranian Azerbaijan and Ahmadinejad has abysmal approval ratings amongst Turkic speaking Iranians? On top of that, I voted in this sham election. Do you know that all votes in Iran are cast on paper and that paper needs to be counted by HAND because you have to write in the code and name of the candidate you are voting for? Mousavi only claimed victory two hours into the vote because his campaign found out that the Interior Ministry was going to go forward and claim that it was extremely likely that Ahmadinejad was going to win, 2 hours into the balloting. You tell me, how do you even count 5.5 million paper ballots only two hours after the polls close? In Tehran it is also policy that the ballot boxes need to be transported to the Interior Ministry before they can even be opened, subtracting even more time from the 2 hours. Facebook does not work, Youtube does not work, basically all communications are down. You tell me sir, if they did not rig the elections where are all the people who supported Ahmadinejad? Why aren't they celebrating? Why is the mood in Tehran, even southern Tehran so gloomy? Why is the government so scared? When looking at these basic facts you can come to the conclusion far more easily than using some stupid statistical analysis that gives legitimacy to a government which for 30 years has just further consolidated its power.
Also, Haukur, the 85.9% turnout statistic is from the 1996 election, if you actually read the WP article you cite. The turnout for that landslide was 63%, as the table in the article plainly states.
Thanks for the updated, Darius. Stay safe.
re: Darius: Stay strong. You and millions of Iranians are in our thoughts (and prayers) today.
Darius, thanks for the report and information. However, Nate is not saying that this DISPROVES the election was rigged, he is just attempting to analyze what is flying around the internet as "conclusive" evidence. I don't think anyone on this site would disagree with your statement, "When looking at these basic facts you can come to the conclusion far more easily than using some stupid statistical analysis that gives legitimacy to a government which for 30 years has just further consolidated its power."
Peace.
I think the usually accurate polling methods that Nate followed during the Primaries and the US election are very suspect here in the way the data was tracked...
There are a whole bunch of penetrating questions and comments in this thread that Silver needs to address...
Please Nate, don't ruin your sterling reputation with suspect and incomplete data from this Iranian election...
It's alright to pose the possibility that this was a valid election, but there are so many other red flags that I think your post here was premature.
More importantly, the Interior Ministry results claim that Karroubi, an ethnic Lor, got crushed among his own base, as did Mousavi among the Azeri? What say you to that, Nate? That seems to make the uniformity of the Interior Ministry's results much more suspicious than they otherwise would be...
Tapir Boy-
How well did Michael Steele do in among Maryland African Americans in his Senate campaign?
It is the strength of the candidate, not the ethnicity that matters.
Nate said, If Moosavi truly did have the support of a majority of Iran's citizenry, the best evidence we will have of that is what happens in the streets of Tehran over the next days and weeks. This is truly the best way to tell. Iran has a very young and increasingly politically engaged population. If there was broad support for Mousavi, I would expect some general unrest.
I just read Darius' comment when I previewed and I guess the government is expceting unrest, which indicates that they do not feel their hands are clean. Best of luck to you Darius.
Okay, Nate, so no one has proven that the vote was rigged, but when you combine the high R-squared with the ethnic anomalies, there is a strong suggestion, and even a rebuttable presumption, that it was rigged.
You've focused on the word "proved," which (by the way) the Teheran Bureau's item did not use.
Step back from the semantics and look at the totality of the situation, and I think in this case the Teheran Bureau has it right and you don't. Yeah, they said it was "impossible" for those results to be real, and you've been able to construct a possibility. But in the real world, I don't think it's possible for the official result to be authentic.
I'm a big admirer of your work, Nate, but even you can get it wrong. This is one of those times.
We have a title change removing "statistical evidence does not prove..." from the headline! Who knew that bloggers actually read the comments, especially when the post is getting flamed.
If Iran had tabulated all the votes, then reorganized them alphabetically by region (or used some other means to deliberately homogenize the results) and then released them in six waves, I guess this would be persuasive. Outside of that scenario, results released in a temporal fashion that show this degree of homogeneity are suggestive of shenanigans (though not, admittedly, conclusive proof).
Then you have the apparently massive protests in the capital . . . protests against an election where 85% of the electorate allegedly turned out to deliver a 25+ point landslide to the incumbent . . .
Another way to frame your conclusion is that in order to produce such a high R-squared you need to draw from the returns at random. That is almost never the case in reality since regional and urban/rural factors figure heavily in both vote and the speed at which votes are counted. So your results could be interpreted as having the opposite implication you give them.
I won't take it personally that my word for verification is 'bongsha'. I may use that as my alias in the future!
re: Jen
"How well did Michael Steele do in among Maryland African Americans in his Senate campaign?
It is the strength of the candidate, not the ethnicity that matters."
In terms of African Americans in Maryland, yes. In terms of Azeris in Tabriz, history has differed. Juan Cole's analysis Nate linked to in his edit points out that Azeris have always voted "disproportionately for even minor presidential candidates" from there. Given that Mousavi was also very popular there in the weeks coming up to the election and Ahmedinejad unpopular, for Ahmedinejad to win outright with 57% of the vote is very suspect. It'd be like McCain winning Illinois.
And thanks for the update, Nate. I wasn't particularly saying you were wrong, just questioned the method. If Iranians are taking time to get through internet blockades to get to your site, you're doing something right. :)
I'm not one to automatically believe that elections whose results I don't like were rigged. I see no particular reason to believe that Iran's elections were rigged...few reasons for that.
1 - By definition, the establishment has to be okay with any candidate winning, since they approved all of them.
2 - Reformers have been elected before, so it doesn't seem that the country's structure precludes a reformer winning.
3 - The Iranian system seems to be designed to prevent revolutions by giving the people an outlet for their hopes and aspirations in the form of presidential elections, without risking the the real power base in the system, the Supreme Council.
Rigging the elections seems like a bad idea given that it doesn't really matter who wins, and by allowing real, fair elections there's a higher likelihood of keeping the country stable.
Overall, I'll never really understand the US's obsession with Ahmadinejad. He spouts off at the mouth, but he has no real power (nor would whoever might replace him) and what happens in Iran has little effect on the lives of Americans. On the whole, the Iranian gov't is no worse - and by many accounts may be better - than other governments that are on "our side," and therefore escape scrutiny.
re: Haukur
The thing about Iceland is that they traditionally have an extremely high turnout. In 1980, the election prior to one you cited, turnout was 90.5%. In 1996 it was 85.9%. In fact the two years you cited were roughly 15% and 25% below the norm and the lowest voter turnouts in Iceland since 1946.
I'm gonna go out on a limb and say this contest was rigged... albeit really poorly. Consider this:
At the moment the polls closed (just about before both candidates declared "victory" like Johnny Drama on a "Viking Quest" re-run), Mousavi's Intrade stock was at about .80 (this is roughly, I'm doing this from memory). Ahmadinejad's was correspondingly at about .21. Then, as the "results" (with a suspiciously strong linear relationship) came out, we saw the two prediction futures very quickly snap to about .50 each, before becoming extremely lopsided overnight. Now, if you plan on rigging an election way in advance, wouldn't you also be the type of person to place a BIG bet on your guy winning? Premedidated election fraud should have been reflected in the predictions markets. Instead, I think we are seeing post-hoc fraud, in which Iranain officials are just calling the election as they see fit, and not taking the time to make the results seem plausibly legitimate to an armchair statistician.
re: ariseatex:
Michael Steele didn't do "well" among African-Americans, but he did perform significantly "better" than Republicans typically perform among African-Americans in Maryland. I looked at the data on this one for a paper in undergrad and that contest is certainly an outlier among blacks when compared to previous U.S. Senate Races in Maryland. Ethnicity matters.
Wow, lots of people giving Nate grief in here. These comments reflect more poorly on the commenters than Nate.
Math is dispassionate.
Nobody here is saying that the elections were valid. We are saying that a high R^2 value of returns over time is not, in itself dispositive.
The truth needs to be determined here, but it need not be built on shoddy scaffolding. The developments in Iran are disappointing at best. Best wishes to the Iranian people.
I am surprised Nate could be so gullible to Iranian propaganda and not take the turnout into effect either
I think Nate's analysis may be correct. I was skeptical myself and decided to run waves by areas of the country.
Wave One: Maine, new Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut
New York, New Jersey, Delaware, Maryland, DC
Wave Two: Florida, Georgia, Alabama, Missisippi, South Carolina, North Carolina, Virginia, West Virginia, Tennessee, Kentucky
Wave Three: Louisiana, Texas, Oklahoma, New Mexico, Colorado, Arkansas, Kansas, Missouri, Illinois, Ohio
Wave Four: North Dakota, South Dakota, Minnesota, Iowa, Wisconsin, Michigan, Indiana, Utah, Pennsylvania, Nebraska
Wave Five: Wyoming, Montana, Idaho, Nevada, Arizona,California, Oregon, Washington, Alaska, Hawaii
When I did this analysis, I received an R-Squared of more than 99%. The graph looks pretty similar to Nate's as well. I would be interested in seeing one state's analysis to see if this trend continues, but it appears to me that using this graph as evidence of election fraud in Iran is flawed.
Having said that, I believe this election was probably stolen.
Polls all closed in Iran at the same time. Counting began everywhere in Iran at the same time. There is only one time zone in Iran. The votes weren't ordered by the race, relegion, region or gender of the voter before counting began. It was pretty darn close to a randomized sample.
Darius, i must congradulate you on your excellent English composition skills. And might I also say how touching I find it that despite all the commotion with all the street protests the explosions near your house (what part of Tehran was that again?), that you would take time out to log on to five thirty eight dot com and update us on the situation.
Masoud
Great report Nate - Here is a potential marker, something I heard as analysis on the news. In comparing Ahmadinejad's 2009 results with his 2005 results, the voting seems to suggest he lost no support, whereas his handling of the economy has been viewed even by many of his supporters as dreadful. So why has he lost no support at all according to the data? There have been reports that ballot boxes weren't even opened and that results were essentially just made up. And why did both candidates claim exactly the same percentage victory, what was it 64%? Very odd Watson!
Except that you don't consider that the results were reported as they came in from the voting districts, not alphabetically. You data suggests that Arizona and Alabama and Alaska all put in their votes at the same time, that California voted before Texas and other southern states. Just saying that next time you waste bandwith to make something like this, at least make your comparison make real world sense, rather than spreadsheet sense.
I did a similar analysis of the US elections to Jeb. This time I simply followed the time zones (5 waves with Hawaii and Alaska lumped together)and got an R-Squared of about 98%. I believe Nate's analysis is correct. The original graph doesn't prove that the election was rigged. Neither does it say that it wasn't...
Just wanted to say that in no way shape or form was I saying that Ahmendinejad is/was a good candidate by saying it is the candidate that mattered. It was just a reflection on Michael Steele.
Ariseatex, I am not saying that the election was not rigged, just that ethnicity is not determinative. I am not familiar with how conservative Azeris are relative to the rest of Iran. If they are a more conservative group than I would think they would be more likely to vote their concious than their ethnicity; that was my main point. However, if they as a cultural group tend to be more moderate than I do agree that it would be fishy in the extreme.
Matthew, I made the original comment regarding the Steele Senate campaign and it may not have had to do entirely with race. Steele's volunteers made a point of putting pictures of Steele on his direct mail pieces and implying he was a Democrat. Nowhere did these mailers mention he was a Republican. He may not have significantly outperformed a white/hispanic candidate without such deception.
Could you not simply take every tenth vote, or every fifth vote, that came in for Moussavi, and count it for yourself?
Cole's take is that it's the "Supreme Leader" who (theoretically) did the rigging and did it in a panic after incorrectly assuming that Ahmadinejad was going to be fine. Because he didn't have to time to properly prepare for the rigging (the theory goes), it was done sloppily, like a murder committed in a frenzy of panic rather than a carefully plotted crime.
On the other hand, if we re-elected Bush in 2004, it wouldn't surprise me in the least if the Iran equivalent of our wingnut trailer trash voted their buffoon back in as well.
Haha moteshakeram Massoud jan. I'm near Vanak in Tehran but in an apartment complex so I can see and hear a lot of stuff even if I'm not really close to them because I'm on the 14th floor. Also, when your satellite TV and phone (for international calls) don't work and only the internet works but really slowly wouldn't you prefer to at least go on there to see what's going on? Today I got to see some of the fires they started in Vali-ye-Asr Square from my balcony. I'm not gonna be TOO specific with where I am because you never know with this government. Things have died down because its pretty late and the internet is faster now, which is good. Fivethirtyeight.com is the blog I read every day back home in Maryland so I read it every night when I'm here too (it's 2:39 AM here right now)
Nate, the said analysis left out an important piece of evidence by, probably, assuming that it was obvious to its readers who followed the election, most of them familiar with the Iranian demographics. That, of course, is the results were revealed wave by wave by announcing rural areas and small towns first, and gradually moving to bigger cities and more liberal areas. What helps that analysis make more sense is to know that according to all past presidential elections, the rural areas favor the more populist, more conservative candidates, and as you go into big cities like Tehran, the results get reversed, especially when the turnout is great. Based on this information, it was anticipated to have more flunctuations as we moved toward bigger cities, say from 70% to 40% or even less. That 70% was too high for many observers to begin with, but if we assume its validity for the sake of argument, a huge turnout in Tehran and few other big cities alone could cancel it out completely given Ahmadinejad's complete lack of popularity there. This can easily be shown by checking the results of similar past elections.
Now if you want to compare that with a comparable scenario of the 2008 US presidential election, consider something like this:
Wave 1: Alabama, Tennessee, Kentucky
Wave 2: Texas, Mississippi, South Carolina
Wave 3: Missouri, Indiana, Florida
Wave 4: Ohio, Colorado, Pensylvania
Wave 5: Iowa, New Jersey, Maine
Wave 6: California, Massachusetts, Illinois
See what I am trying to show? I am not suggesting such scenario is plausible in any sense, but the point I am trying to remind you is, in a comparable US scenario if you were to get the results from red states earlier and from blue states later in the process, you wouldn't expect to the same ratio to maintain from wave to wave. And this is what's happened in the Iranian model.
Mr. Silver, for a guru of statistics, you seem to be amazingly naive comparing US and Iran as if you are comparing French and US elections.
May I inform you that Iran politics are driven by tribal, religious, educational, even clan differences, not just politics, like in the US or France! While different counties in TX or RI have population somewhat similar to each other, this can NEVER be so for different parts of Iran!
http://www.salon.com/opinion/feature/2009/06/13/iran/
According to Juan Cole...
Obama administration officials were privately casting doubt on the announced vote tallies. They pointed out that it was unlikely that Ahmadinejad had defeated his chief opponent, Mir-Hossein Moussavi, by a margin of 57 percent, in Moussavi's own home city of Tabriz. Nor is it plausible, as claimed, that Ahmadinejad won a majority of votes in the capital, Tehran, from which he hails. The final tally also gave only 320,000 votes to the other reformist candidate, Mehdi Karoubi, who had helped force Ahmadinejad into a runoff election when he ran in 2005. It seems odd that he get less than 1 percent of the votes in this round. Karoubi, an ethnic Lur from Iran's west, was even alleged to have done poorly in those provinces.
I disagree with what Nate was saying in that the order these results come in matter: there are going to be hotspots for Ahmadinejad and others for Mousavi. It should also be looked at how candidates Rezaee and Karroubi did in their home districts and how the turnout and voting patterns hold across Iran. For example, in the 2004 Ukraine presidential election (which was rigged for the anti-western incumbent president) it had significantly lower votes for Yushchenko in his territories and extremely high turnout in Yanukoyvych strongholds (i.e. some 90%+ votes with some 90%+ turnout).
Dariush jan,
Khasteh nabashi! You can't blame a guy for asking can you? I hadn't heard about any explosions is all.
I say forget the advice given here, go out and give em hell tomorrow if that's what you believe, you probably don't often get the chance to do that. God knows i don't.
While Nate's breakdown of the graph does appear solid, I see no reason why Mousavi would loose the Azerbaijani vote in his home province. Ethnic Azeri always vote along demographic lines, even for minor candidates. Similar it seems unlikely Karroubi, an ethnic Lur, would lose those territories. Furthermore, it seems unlikely that he would receive less than 1% of the vote when he received 17.24% in 2005. Sure, he probably lost some support to Mousavi but I cannot imagine a scenario in which he would receive less than 1%
Your assessment is completely flawed. You have no understanding on the ethnic distribution of the Iranian population and trying to assess this from a highly linear model to extrapolate a very non-linear vote pattern highly sensitive to geographical location and ethnic makeup is simply flawed. Have a nice day and stick to things you understand. This can not be diagnosed with primitive statistics and linear algebra 101 reasoning
Folks, this post isn't meant to show that the graph is necessarily correct, and it's not a commentary on the specifics of the Iranian election. All it is showing is that the linear progression (or at least the appearance of it) being shown should be expected in a random sampling (ie, unless there are extenuating circumstances such as one candidate's strongholds coming in first). If there are such extenuating circumstances in the Iranian election, then the graph is not even the clearest evidence of tampering. For example, rather than saying "there shouldn't have been a straight line because Mousavi should have won the cities, and most of the early votes were from cities", all you have to do is say "Moussavi should have won the cities but he didn't." It appears that there really were unexpected-to-the-point-of-incredible results in certain areas, so it's really not worth spending so much effort defending the significance of this graph.
Hi Nate
the improbability of the stats is clear specially when compared with the vote-counting trend of the past 20 or so elections in Iran. Traditionally, the tallying of the votes starts from very small towns and villages which usually favor the conservatives and the bigger cities and the capital are always the last votes to be counted and tallied due to their massive populations. In all the past elections the conservative candidates start with more votes and as the bigger cites are counted the slope drops significantly, which here is obviously not the case. However, even disregarding this, the accumulative weight of evidence leaves very little doubt for anybody who participated that a massive manipulation has occurred.
cheers
B from Tehran
/me looks forward to the catnip like effect of Nate's analysis on the acorn crowd.
They have not even counted the votes. They are so stupid that they basically used simple statistical technique to show Mr Ahmedinejad has won with more than %50 of the vote everywhere and fudged some numbers together based on supposedly what the vote was. Such perfect data distribution is impossible unless you are using computers to direct flow controlled air traffic. That my friend is how one detect fraud from unusual patterns.
I wonder how many people here in the comments are also convinced that Bush stole Ohio in 2004.
The chart that is going around is SPECIFICALLY DESIGNED to be misleading. An honest chart would just report the percentages for each batch, rather than summing things up as it went.
re: Drew Miller
The Ohio 2004 analogy would hold merit if Bush somehow won in even the heavily Democratic urban centers. If Ohio was somehow rigged (which I don't think it was), even Rove wouldn't be stupid enough to make Bush win everywhere by a huge margin. Ohio is high in everyone's mind precisely because it was so CLOSE. But the official results here have him winning even in opposition territory.
I'm becoming more convinced that the chart itself may be flawed, but let's not throw out the overwhelming evidence mentioned by other commenters suggesting a rigged election just because one graph isn't as clearly rigged as some of us originally thought. Even Nate recognizes that in his post. (BTW, what does this say about Nate's work here that people actually care about the statistical details of an election miles away? I for one probably wouldn't care as much for the numbers if not for this site).
Drew,
You made me laugh!
"The chart that is going around is SPECIFICALLY DESIGNED to be misleading."
So does that qualify as a bit of a conspiracy afoot, to mislead?
One argument I have heard is that rigging this election would require too widespread a conspiracy to keep it secret. I wonder if the rigging was so crude (see Juan Cole) precisely because it was done by just a few people.
There already people from the interior ministry ( the ones that actually run the elections) coming forward saying this was completely rigged. The votes were never even counted. Period
Statistics is applied mathematics. There is an element of judgment involved, an example being when judging correlations and their relationship to causality.
I can't argue with Nate's point that no one has proven, in a mathematical sense, that there was fraud. However, in applying the data to the situation at hand, the count is suspicious as hell.
Nate, I think you should re-write your posting. You get an A for the math, as usual, but a gentleman's C for your application. This was not your best work, my friend.
Let me second what Drew Miller said above. You really want to see Ahmadinejad's vote share in each newly counted batch. If you do this, you get
Wave 1 70.40
Wave 2 65.68
Wave 3 66.21
Wave 4 66.29
Wave 5 63.93
Wave 6 62.28
In other words, Ahmadinejad's share of the newly counted vote trended down, though neither linearly not monotonically.
This does not prove the election was fair since (as many others have noted) we need to know more about which areas reported in each wave. But it does belie the graph's implication that there was a winning margin fixed from the get-go or that there was no variation over time in the returns.
http://english.aljazeera.net/news/middleeast/2009/06/2009613121740611636.html
I agree with Nate that the number alone is not enough to determine if there is fraud. The 'swing by district' would be a better indicator. I mean, to achieve 66-69% from every district?? That would be like Obama carrying Alaska..
technically you are right, but as Churchill said, there are lies, damn lies and statistics.
So, overall I might agree with you that using that graph as a proof for anything is not the best idea.
However, as again others have pointed out, the waves must be looked at more from rural to urban than anything else.
I will take the example of Germany and in previous elections. in Germany likewise the first results are from rural areas and then come urban areas and I have seen the Socialist Party in their better days catch up on the Conservative Party on about 5-6 points during the day. Now, add to it that the difference in this election is a bit more extreme as Mousavi's strong bases were the cities who come in late and around 67% of the population live in urban areas.
.998 vs .996 might not seem like a lot, but it shows twice as much variance from what would be calculated from a perfectly straight line. Considering the .996 came from an unrealistically uniform scenario, and more realistic scenarios yield numbers more in the .98 to .99 range, I see only one conclusion:
The election was rigged. Sorry Nate.
Ray has just explained what I was going to write. .996 is 100% more variation than .998. Furthermore, the United States had a far more homogenous electorate than Iran. Even a 'very safe' state in the US was 60/40. There is much greater variation in support across the Iranian provinces.
Again, this does not prove fraud. I really think Nate needs to urgently compare this to opinion polling, and try and reverse-engineer the results to try and get some coherent answers about the likelihood of this result. At least, it would be very interesting and as important as anything that's ever been posted on this site.
While you are right that the particular analysis you were responding to is flawed, most people will wrongly interpret your refutation as claiming that the Iranian election was legitimate. This is irresponsible; you should withhold meta-analysis until you have a direct analysis of the question everyone cares about, which is whether the election was rigged or not. We don't know, and we need data! Shooting down pieces of non-evidence doesn't help.
Why is the first group of states chosen to be 33% of the vote? That's close to twice the first wave percentage in the Iranian "results" and it's in the earlier returns that one would expect the biggest variation.
Unfortunately, this is perhaps the weakest analysis I've ever seen from 538 - it's classic missing from the forest for the trees. While Silver talks about an irrelevant statistical flaw, he doesn't bother to mention that an election polled as a dead heat is now apparently won by more than 30 points. You don't need to be very smart to see that this wasn't an honest election.
Great post... but this is not the main reason that we say the election is rigged. What we should realize is that the 2:1 ratio persists across all the regions and states (unlike McCain vs Obama). Even the home states and cities of the opposition candidates report the same ratios. This is unprecedented. Also, given the huge network of the people that we're connected to (esp. with the help of facebook and similar networking sites), we don't know that many people who have actually voted for Ahmadinejad (unlike 4 years ago when he was popular mainly due to the huge resistance against his rival).
Are the precinct by precinct data out yet? They should be statistically abnormal if the results are a construction -- things like too even, or too many instances of a particular final digit in the overall vote count -- people down low in the food chain have to signal to higher ups that the election has been rigged in their area somehow. In Taiwan this was traditionally done by stamping the ballot in a particular spot -- on the candidates picture, for example, if your vote was paid for by X, you stamped on the right eye, if paid for by Y, you stamped on the mouth, so X and Y's boss could make sure that they had done their jobs. The ballots are publicly counted in Taiwan and anyone can watch (I have observed the process myself on several occasions) so it would be easy to verify with the Mark I eyeball whether the vote buyers had done their jobs. The Central Election Commission ended this system in 2004 by tossing out ballots with stamps on the photo faces, but other methods remain.
To verify the cheating -- and it looks extensive from my vantage point -- individual ballots will have to be examined, and the precinct by precinct counts carefully analyzed for odd patterns in the numbers.
Michael Turton
JTrue and George -
Part of the problem was the pre-election polling was all over the place and done primarily in Tehran. There really is nothing to compare nor does it prove anything.
At this point, I think there is not a whole lot of evidence either way. The bottom line on this is it is not any of America's business. Putting our noses up in Iranian elections isn't a good way to win hearts and minds and just helps Ahmedinejad, Khamenei and the extremist element in Iran cling to power. You would think we would have learned our lessons when Bush's posturing led to Ahmedinejad's election in the first place. In the absence of proof, we should be careful of flinging accusations when a wait and see approach is better.
A more valid concern is how the protesters in Tehran are being treated at this point and the one on which the government should be focusing.
Nate, this analysis is shallow and does a huge disservice to the many Persians who are trying to get word out that the election was fraudulent.
My Persian friends tell me that election results come in in smaller areas before cities -- pretty much how it happens in an individual state in the U.S.
You should have done your analysis on a *single* state, not the country as a whole. And you should use a selection mechanism that mirrors how results would have been reported in Iran -- i.e., don't randomly select counties. Select the smaller ones first (if this is indeed reflective of how the vote was reported in Iran).
I'd put good money on the fact that a graph like this using real data for, say, Illinois, would not at all be a straight line.
I'm sorry to be negative, but I have a lot of friends who are crushed by what happened in their country, and as a prominent voice in the media for analyzing statistics you have a responsibility to do better than this.
doesn't it matter that the US election is composed of ten times as many cases? in each data point your averaging across tens of millions of votes, while in the Iran case millions. wouldn't you expect the variance in the US example to be much smaller anyway?
Silver will get a lot of hate mail for this piece, because Obama fanatics have agreed that Ahmendinejad is mean and ugly, therefore he won the elections, and the other guy has been compared to Obama, therefore he won the elections because if you are compared to Obama then it means you are good and you have elections stolen from you.
Progressive, I don't mind who won. American interference in Iranian politics has caused nothing but trouble in the last 60 years. I do however mind math being badly applied to a real life situation.
Interesting analysis. But as mentioned before, you leave an important factor out. You assume that votes are more or less homogeneously distributed which is not a bad assumption when you look at the states as a whole. If you had done this analysis for four waves of urban or rural areas in red or blue states you wouldn't have gotten same ratios.
That structure of waves is in reality close to what happens in Iran. Smaller (and more rural) provinces finish their voting earlier. Their counting and reporting happens first. Larger provinces, and larger cities in those are last. Composition of votes in those "waves" is completely different. The same phenomenon exists in vote composition for, say, Houston and Austin vs whole Texas. If your waves are Texas minus Austin/Houston and those two cities, then your ratios won't produce a close to unity R-squared.
I think it should be obvious to political junkies that results released over time are not the same as results released in random groupings like states. I imagine most of the readers on this site have spent time huddled over the exit polls, right? When we watched those exit polls come in, we always had to pay attention to where the results were coming from, knowing that would vastly change the results.
To put it another way, we all knew that Obama had sealed the election before seeing the tallies from the west coast. Why? Because we knew California was his strong territory and knew that he would surge when those results came in. In the iranian elections no surge was seen. In a fair election the pro-Admadinejad and pro-challenger voters would have their results come in at different times.
Am I missing something? The data reported shows Ahmadinejad with a huge initial lead, that's when smaller vote districts would have finished counting, and that lead slowly dwindling as the larger cities finish reporting. This is completely consistent. The US example was just to show how such a graph that has ridiculously straight line of best fit can be constructed for any data set, not to draw some kind of crazy direct analogy between the voting pattern of the two electorates.
I think people need to chill with the race analogies and supposedly super-fractured nature of the Iranian electorate as well, most of it is a bit displaced from reality. Not the sort of thing to comment on casually.
The district by district results are going to be released sooner or later, and then everyone will have the chance to sink their teeth into some real data.
Masoud
masoud,
Iranian electorate is super-fractured, and I doubt anyone familiar with Iranian politics would argue with that. District-by-district results, as you put it, were always reported as they became available. This is the first time that only totals were given without any breakdown.
This analysis is silly. Obviously if you stratify a population by some randomly-assigned grouping (eg, state letters), you will get groups that have very similar characteristics (such as vote ratios). The point of the graph is that election results are never reported randomly, but instead always follow some demographic characteristics (such as proximity to urban vote-counting centers). I don't recall ever seeing an election where the returns reported multiple times along the way exactly matched the final results. The point is, no plausible reporting pattern would every produce such matched ratios -- and random reporting is about as implausible as the idea that real, non-random reports would all have the same ratio.
Here, I did a better analysis, breaking the U.S. down by region and graphing results as if reported by region, cumulatively.
Note that this analysis is still flawed, since we're using four times the number of people as in Iran, and each region is a mixture of demographics itself, which may or may not be the case for Iran's results. But at least it's better.
There are greater deviations from a straight line, although still not huge (large deviations are not expected for such large numbers of people covering so many demographics). You can judge for yourself whether you think those deviations are large enough to still reject the Iranian graph as unconvincing:
http://spreadsheets.google.com/ccc?key=rWTV3yvh2o3RMO5uwtbe7RA
The Times of London has some very relevant information in today's edition. They claim to have seen internal polling done for the Ayatollah, which showed the opposition winning "at least" 58% percent of the vote. Instead, they supposedly won only 34% in a fantastically high turn out election. Nate should crunch the odds on that.
Amir,
I don't want to get bogged down in semantics with you. There are many demographic and linguistic divisions in Iran but they are all superficial and subordinate to a unifying culturural,Irainan identity. It is not unlikely at all for the Azeri-speaking minority to vote for Ahmadinejad, or for someone like me who is part Lur to never be able to bring himself to vote for a corrupt loud-mouth like Karroubi. I wonder why no expert on the super-fractured, racial nature of Iran has come forward to suggest that the Majority Persian ethnicity would never vote for a Turk like Mousavi? Economic and class divisions are much more pertinent.
Racial bigotry has very limited purchase in Iran. I believe giving people the opposite impression has more repercussions than setting the stage to advance proof of fraud.
Mousavi is no coward, he's not backing down and he's got eyes and ears all over the Interior ministry, not to mention observers at polling places all over the country. Whatever has or hasn't gone on, we'll get to them bottom of it sooner or later. No need to be hasty.
Take care,
Masoud
Progressive, (who I suspect is actually one of the neocons like Daniel Pipes who is actually rooting for Ahmadinejad) it's not "hate mail" to criticize Nate's analysis. It's criticism.
I think 538.com is a magnificent site. But no one, including Mr. Silver, is immune to error or criticism. I think Nate has overreacted to some of the language that accompanied the graphic, specifically the statement that it is "impossible" for the official results to be honest.
In his attempt to show that the results could theoretically be honest, Nate went and cherry-picked U.S. election results that didn't even match the pattern of election reporting here, much less be a useful analog for describing what is happening in Iran.
Nate, I really hope you will step back and take a thorough look at your treatment of that information. Your addendum to the original post is unsatisfying and defensive. Don't be too proud to admit a mistake. That way lies Washington, D.C., and everything we despise about it.
As for you, "Progressive," it's true that most people who are looking at Iran would like to see a change there. At least the normal people want that. Then there are the neocons, who despise Obama so much that they are siding with a hostile leader who wants to obtain nuclear weapons. It's bizarre.
But the amount of interest on this blog, and the level of criticism, doesn't approach some of the critiques of Nate's statistical methods levied during the 2008 election. You weren't here for that "hate mail." You were probably posting hate mail of your own on Commentary magazine's website.
NATE PLEASE CONSIDER ADDING NEW ANALYSIS SHOWING OTHER SCENARIOS. John's comment from June 13, 2009 11:54 PM contains complementary analysis of the US elections with R^2 ~ 0.994 and more variability in the cumulative reporting. Your post exaggerates a very improbable scenario, as can be seen by looking at a sample of the comments. I think your post is, frankly, dangerous in the current format - I am not advocating censorship, I am only asking for a more balanced analysis of what is happening. Your post has been picked up by the NYT and others and will surely be used as "proof" of fairness in the election unless you expand it.
At this point I'd agree with Nate. Yes, the large R^2 looks impressive but without knowing 1)how the actual returns came in and 2)the decision making process as to when/how results were announced it's impossible to definitively conclude, based on the analysis, that rigging took place. Really, it's (the R^2) the wrong tool for the job.
Where's Andrew Gelman when you need him?
John,
Nice, but why not simply write a quick program to determine which states, in which order, maximize the sum of squared residuals?
Rather than pecking through permutations one by one, I mean.
Sherifffruitfly:
The first order was taken from a commenter in a Reddit thread. The second was randomly selected.
The data are there for you to play with as much as you want. Go try to make a real point with them rather than just laying down an unsupported smear against me.
When my son told me that Ahmadinejad and asked me if I thought the election was rigged, I asked him what was the vote totals. When he told me that Ahmadinejad allegedly won 62% of the vote, my answer was "yes".
Tehran and its environs represent about 55% of the voting Iranian population. Considering the voter turnout in Tehran, how much it represents the country, and the difference in size and enthusiasm of the political rallies between the two candidates, it strikes me that Moussavi would have won an overwhelming victory in the Tehran area and environs.
This doesn't mean he would win the vote. No more that Kerry's support in New York and other major metropolitan areas meant that he would win. However, Ahmadinejad would need massive support in the outer reaches of Iran to compensate (something he probably had), and the vote total would have been closer to a 52% to 55% victory.
Your analysis of the vote totals was interesting. What was missing is where the vote count was taking place. You purposefully chose states that would have kept the vote in close alignment, but that's not what happened.
Instead, the East Coast (where Obama was the strongest) reports first. Then, the Middlewest and Southern states begin to report which helps the Republican vote counts. Finally, the West (which again helps the Democrats) report.
The question is how were the votes counted. I would assume that Tehran would be one of the first places totaled due to its central location and density. Then, other areas from around the country would have come in. That would mean that Moussavi would have done better at first with his percentage shrinking throughout the night.
What would be interesting would be to compare the totaling of votes this campaign to previous campaigns.
@ sr27182
Your post has been picked up by the NYT
Where did you see that?
The standard deviation in this data is apparently .119 - is this important? Apparently this graph is strange, but I have no idea how strange.
I'd love to see this graph pulled to bits and more work done on it. Please Nate?
@Nate -
I think your using waves of states organized in alphabetical order has had the undesirable effect of canceling out regional variation. If you had done your analysis on a per-region basis, I think you would see much more variation.
If the waves of election results in Iran were not of regions that had been shuffled in this way, but were aggregations of regions, I would find the original analysis compelling.
@Opus 132
NYT quotes Nate at 5:51 pm (thelede)
http://thelede.blogs.nytimes.com/2009/06/13/landslide-or-fraud-the-debate-online-over-irans-election-results/?hp
Sure, that is the NYT blog, but still, it was linked from the front page just a few hours ago.
Another important difference between the proposed US scenario and the Iranian election results is the size of the electorate involved: 130 million voters participating in the US vs. 30 million in Iran.
Skepticism is good, and warranted in this case, clearly. I'll admit to naively being convinced of foul play at first glance of the Iranian results graph. Now, although it still seems quite likely to me that election fraud took place, I also recognize that I really have no clue how much information this graph is providing me. Unfortunately, that question, of how this evidence affects the probability of our hypothesis that election fraud took place, is very difficult to answer. If and when proof of fraud comes, it will come by other means.
Let's say someone wants to generate a data for an election. I would certainly take into account that the votes should have high correlation. What I might miss is the point that Nate has missed too. I should not generate it like I know the ending!
In Iran actually the rural areas report their result first, so the first head start for Ahmadinejad is expected, a quote from Ahmadinejad "Iran consists of many villages and countrysides and some big cities should not be considered as Iran". So when a real time report is being given and it is specifically stated that in the first wave the rural and in other waves bigger cites votes have been included, it should not look like this.
There is joke with our Iranian friends, "One day after election, The Minstry of Internal Affairs Stated: We are sure that there is no mistake in vote counting, we have been counting the votes several times in the last 20 days".
Iranian Good luck
Wave 1 70.40
Wave 2 65.68
Wave 3 66.21
Wave 4 66.29
Wave 5 63.93
Wave 6 62.28
It's clear from reading the comments that the overwhelming majority of those criticizing Nate's analysis did not realize that these are the corresponding percentages in the graph at issue.
I wish I'd read the body of his post a little clearer because it took me until Ken's comment to understand this as well.
Nice job Nate, the edit should've gone at the front of post, btw because that's the most important point I think.
@ sr27182
Thanks,I see it now.
BTW,on Friday afternoon the Times reported that,two hours after the polls closed, the official Iranian news agency stated that Ahmadinejad won in a landslide.Enough paper ballots counted and reported
in two hours to declare a landslide!
You don't have to be a statistician to recognize that the fix was in.The fact that it was so unbelievably clumsily done almost lent the phony results some credence.The fixers should have hired Robert Mugabe to design the scheme.
I suspect it impossible to determine if the election in Iran was representative. The breakout by region, by Persian versus non Persian likely not available. What influence strong armed tactics may have had, unknown.
If reports over the past several years of high unemployment and horrible economic conditions are true, it is hard to believe the outcome. If that happened because of stupidity or a rigged election is unknown.
I must admit I am not upset with violent protests within Iran.
Progressive said...
Silver will get a lot of hate mail for this piece, because Obama fanatics have agreed that Ahmendinejad is mean and ugly, therefore he won the elections, and the other guy has been compared to Obama, therefore he won the elections because if you are compared to Obama then it means you are good and you have elections stolen from you.,
BULLSHITE. It has absolutely nothing to do with Obama.
http://www.nytimes.com/2009/06/14/world/middleeast/14iran.html?_r=1&hp
We all know that there was voter fraud. But I still wanted to analyze the numbers to get a back of the envelope feel for how much fraud there might have been.
I made some strong assumptions and am in no way a statistician. However, I feel that these numbers are reasonable:
Iran’s Interior Ministry said Saturday that final results gave Mr. Ahmadinejad 62.6 percent of the vote, with Mr. Moussavi receiving 33.7 percent. The ministry says turnout was a record 85 percent of eligible voters, with more than 46 million people casting a ballot.
If 46mm is 85%, then the total eligible voters is 54mm. I will presume that turnout in previous elections may be closer to 50% and that the population in '09 is the same as '05. 50% of eligible voters is 27mm. Accordingly, if 46mm voted, and the 27mm showed up again, that means that there were 19mm new voters.
Ahmadinejad's supporters have been described as very loyal and ones that consistently turn out to vote. If we presume that Ahmadinejad's vote share was 2/3 of the 50% number (27mm), we get 18mm voters. We also presume that the balance of the 1/3 (9mm) is split between Moussavi and the rest of the field (a strong presumption). This gives Moussavi 4.5mm votes.
Conversely, Moussavi's voters were very excited and new voters. We'll presume that Moussavi got 2/3 of all new voters (19mm), or 13mm. Further, we presume that Ahmadinejad got 50% of the balance (6mm) and the rest goes to others. This gives Ahmadinejad 3mm.
Using these presumptions, the totals for each candidate are:
Ahmadinejad: 22.5mm which is 48% of the vote
Moussavi: 16mm which is 35% of the vote
To win, a candidate needs 50% plus 1. If this does not occur, there is a runoff between the top two candidates. According to the Interior Ministry, Ahmadinejad got 63% of the vote making Ahmadinejad the absolute winner.
I won't recrunch the numbers but it doesn't seem possible that Ahmadinejad got 63% of the vote. Furthermore, my numbers, if at all accurate, indicate that Ahmadinejad probably got a majority but was shy of the 50% win. Finally, my numbers aren't that far off the official tally for Moussavi.
i live In Iran
we hate Ahmadinejad more than you do!
If You want a proof you can see peoples on streets before election and after that.
if we choose ahmadinejad why we are sad and disappointment ?
If people elected him what just only little groups of people ( some 10 to 50 people groups) was happy on streets carrying his posters?
If he was Iranians choise why people was shocked after results???
why two days after election a celebrate take place in Iran?because people was not there.government held this celebrate!
IT WAS A REAL COPU.
Do you know newspapers are controlled after that.do you some of them are closed?do you know SMS in Iran is closed after election.do you know facebook and youtube are filtered? do you know Mosavi's site is filtered ??
I forgot this:
please read this
"Anatomy of Iran's Right Wing Coup"
Just google for It It is filtered and I can not give a link
your last sentence:
"But I'll be keeping an eye out for other approaches, particularly from those who have a deeper understanding of the Iranian state than I do."
I think Juan Cole qualifies, and since you have chosen to stick your analytical nose into this tragedy, maybe you can look at the starting regional anomalies, particularly how reliable it is for a candidate to get big majorities from his home town region.
thanks
the real count as reported from officials from within the "leaders" office leader.ir is as follows .
Muosavi 20 million
Ahmadinejad 10 million
Karoubi 7 million
Rezayei 3 million
Thank you for your work. I am truly embarassed the desperation of Moussavi supporters. In a democracy you not only vote, but you accept a loss.
Not all Iranians are rich Tehranis.
Nate's analysis is just as flawed as the Iranian original. The reason that the released results prove fraud is because a truly random count of votes must fluctuate in "waves." Why? Because support varies by region, and vote reporting is staggered by region. As a previous post stated, "Try the same analysis by time zone and see if the pattern holds." It will not.
I hope Nate Silver doesn't work in statistics.
It will. I just did it, r² = 0.997.
About 42 million people cast hand-written ballots in an election that the winner was declared 2 hours after the polls closed. I know the results came in waves but I have counted pennies and this timeline seems impossible.
Remember in the 2009 Ohio primary when Cuyahoga County took over 5 hours to report their results?
There is fraud in the Irani timeline.
I've been playing around with some of the ordering that other posters have suggested. I imagine that the most extreme change you could get is if you were to sort the results by Obama vote share. Even doing this you get an R^2 of 0.9795 if you use all the states and 0.9866 if you break into 6 waves similar to the Iran graph. You might get different results with different wave splits, but the R^2 stays high.
That being said, other pieces of evidence do look like election fraud is likely. However, as Nate said: this particular graph is not evidence of such fraud.
I'm surprised that Nate (or other posters as far as I can see) did not clearly point out that the true flaw in the analysis is the fact that the individual pairs of scores are NOT INDEPENDENT because they represent cumulative totals -- this violates the assumptions of a correlational analysis.
As many have already speculated, election results in Iran are not reported randomly, but in an order, i.e. rural areas first and then urban centers. Unfortunately, no by-province vote counts were announced to study this matter deeper, although this is very suspicious by itself, since such data has always been published in Iran.
The most important reason that shows the election was fraud, however, IMO was that the very high turnout should have been extremely in favor of Musavi. The reason for this is that there are many Iranians that usually don't vote in elections as a sign of protest. In the last presidential election (in the run-off poll), the turn-out was 48%, so I can reasonably assume that the additional 38% in this election certainly did not vote for Ahmadinejad. Many of these people were first-time voters (as we encouraged many people to vote this time) and it is not sensible to think they would cast their first vote in favor of a hardliner.
The only thing I can say here and now is that the election wasn't fair and that the stated results aren't based on the actual number of votes that came in. I don't think anyone besides the government would say otherwise.
Determining whether or not the statistical evidence is proof of fraud seems to be besides the point if you ask me.
The most conclusive evidence would normally come from international observers, which were absent in Iran.
Rigging elections is fairly commonplace in the world, and we must remember that the US refused to allow international observers during the bush/Kerry election and that there were issues with diebold machines, for example.
A government in a situation like Iran's can easily rationalize election rigging in a crisis context. Not justifying their disregard for the democratic process, but simply saying that I wasn't surprised that they don't seem to have bothered to count votes or to even try to give the election any pretense of legitimacy.
I would say that the most reliable report we have to go on is the poll conducted by terrorfreetomorrow.org, before the election.
http://www.terrorfreetomorrow.org/articlenav.php?id=5
The NGO, the poll and its findings are certainly conversation starters.
Interesting work and good analysis, but as an Iranian I'd like to mention some worries about your analysis:
1-As others have said, you obviously randomized the sample, which will definitely result in the chunks being representative of the whole. In the case of Iran's election, the results were reported in a different manner. Ridiculously enough, the government never published the results province-by-province so no one knows what was going on. But if they were really counting something, they must have started with the rural areas and small cities where the votes are less in number and the polls close sooner and therefore report sooner. It was BY NO MEANS an after-the-event splitting up of the sample into waves. Time zones aren't reliable either because there are rural areas and large cities on the same time zone in Iran. Remember that the small city-big city (the order in which votes were counted) must highly correlate with Ahmadinejad-Mousavi popularity, which it doesn't on the published results.
2-There were 13 'waves' or announcements, not 6. The first 6 waves (~23 million votes) only represent about 60% of the whole votes (~38 million votes). However, the extremely linear relationship kept up until the end. Try splitting up your sample into 12 waves or so, start with the southerns states and end with the northern states. You won't get the same results.
3-The difference in Obama variance in your example and Ahmadinejad variance in the real case is quite significant. Ahmadinejad's vote share varied only by 8%, while your example shows a variance of 12%.
4-There are other statistical peculiarities. Feel free to check out my list of peculiarities here:
http://i41.tinypic.com/wjfa6g.gif
For example: Karroubi received an impossible vote, Rezaee's vote actually decreased once (in the eleventh wave)!! I think no one, even our frenzy supreme leader will not be able to explain this one!
5-As for the point regarding the high turnout, I guess this is what the Iranian-American person means: Usually when there is an extremely high turnout in Iran, it means people are extremely disgruntled. Thus, the incumbent could'nt have been that popular.
To all those who don't think the election was rigged.
Here's a link to a free and fair electoral landslide. The winner kicked the loser's tail as bad is it can get whooped and still didn't get 60% of the vote and the loser still managed to carry his home turf.
Forget statistical analysis...Know BS when you smell it.
http://www.uselectionatlas.org/RESULTS/national.php?year=1984&f=0
This is truly sad that the election appears invalid. The top report is that 10 million votes were added to Ahmadinejad, which would give Mousavi either the victory or a slight edge for a runoff. I was thinking that votes were taken from the other two candidates because they received too few votes in my opinion.
I really hope these riots either turn into something big or something else occurs. There's so many things that could happen. Rafsanjani, who lost to Ahmadinejad in 2005, and is a powerful cleric could do something. The sparks of a revolution have started. We just need to see if it turns into a flame...
Nate, could you do another post examining firsthand what the chances of the election being rigged are?
Shaahin, thank you for a disciplined and reasoned response to Nate's flawed analysis and mistaken conclusion.
You're all wrong (except for Sean)! If the data are cumulative vote counts, then there is a built-in correlation since the points are not independent.
Redoing Nate's analysis by using points for each "wave" independently, you get an R-squared of .86. High, but not nearly as high as the almost-perfect correlation Nate claims.
Now, if someone can point to the Iranian vote count data, we can do the right comparison.
Hi
I invite you o do the same computations on the data provided over 366 different cities on the official website in the end of the comment.
the votes show over 0.9 which is absolutely impossible given the ethnic diversity of Iran.
http://www.moi.ir/Portal/Home/ShowPage.aspx?Object=News&ID=e3dffc8f-9d5a-4a54-bbcd-74ce90361c62&LayoutID=b05ef124-0db1-4d33-b0b6-90f50139044b&CategoryID=832a711b-95fe-4505-8aa3-38f5e17309c9
I just translated the statistics published by the Iranian Interior Ministry for you. Sorry, I didn't translate the city names, that would have been a lot of work. But I guess the province names will work.
http://spreadsheets.google.com/ccc?key=raU4EOsYbOx7WusgF018Xig&hl=en
A cursory look at the data doesn't make me less suspicious. There are unusual variations in Mousavi/Ahmadinejad votes from one small city to another in the same province with the same demographics, presumably to provide the uniform ratio in total
In a previous post I asked Nate to split up the US sample into 12 waves. I'm wondering if 36 waves would be more meaningful, comparing the population of United States to that of Iran.
The correlation is spurious. The fraction of votes for Mousavi is approximately (1.0 - fraction of votes for Ahmadinejad). The plotted data are not independent variables, and so the correlation is necessarily high.
This does not at all address the question of how a race "too close to call" on Thursday became a landslide (in either direction) on Friday. Do I think Mousavi was robbed? Good chance, but one would need to look at the actual ballot counts, probably by region (to the extent that rural Iranians might be more conservative that urbanites) to get some statistical justification.
Am I missing something? It's not about correlation, it's about the RATIO. The ratio of Ahmadinejad's votes to those of Mousavi shows their popularity in different regions. The fact that the ration remained constant across the 13 announcements means these two guys had the same popularity everywhere in the country.
They did NOT have the same popularity everywhere in the country in any way, shape or form.
Therefore, the results are fake. If you ask me, they did not change the numbers, they made up their own numbers from the get-go.
Regardless of questions about that initial graph (which I think we all agree is neither illuminating nor illustrative of fraud), the data provided by Shaahin a few posts above are interesting.
I note from a cursory glance at the spreadsheet two things of mild interest:
First, the ratio of votes received by Ahmadinejad to those received by Mousavi, by city/county, is entirely uncorrelated with the population of the city/county (as measured by Total votes). Second, the ratio of invalid to valid votes is also uncorrelated with population/Total. One might expect either of these to be correlated with population size (the latter generally is), though I know nothing about Iranian demographics. This certainly isn't definitive of anything -- there may be a simple explanation -- but it's intriguing, I guess.
Darius is an Israeli spy.
And you people all need to get out more.
Shaahin,
Thank you for the data.
I'm trying to do a more rigorous statistical analysis to look for evidence of fraud. But I have trouble finding data, and you seem to have access.
Please email me at dms@the-beach.net
Shaahim, thanks once again for your contributions for their data, analysis, and interpretation. Please keep your insights coming. This is an excellent discussion and I think you are one of the best contributors to it.
Shaahin, actually, the ratio didn't remain constant across the announcements -- and it's evident from the data you posted that their reported popularity isn't the same everywhere in the country.
That isn't to say that the results are plausible (I wouldn't really know, but they seem pretty strange to me), just that this particular argument doesn't shed much light on their plausibility.
Karroubi is the key to proving this vote a fraud. In 2005, he received 5,070,114 votes. The 2009 returns claim he now received 333,635 votes. Does anyone really believe that 4,736,479 voters, 93.4% of them, changed their allegiance or died? This assumes of course Karroubi did not pick up a single new voter. In comparison, Ralph Nader, who's fans were extremely peer-pressured to vote for Obama, increased his support, from 463,655 voters in 2004 to 738,475 voters in 2008. Has any candidate for a national office ever lost this high a percentage of voters in one election cycle?
The suspicious consistency of the results looks like an artifact, perhaps caused by aggregating the vote into several large waves. Unlike the US, Iran does not have four times zones with divergent voting patterns.
Take a look at the more detailed spreadsheet posted by Shaahin above:
http://spreadsheets.google.com/ccc?key=raU4EOsYbOx7WusgF018Xig&hl=en
Ahmedinejad's percentage varies from 17% to 98%, and is below 50%in two areas of Teheran.
I do not doubt that there were irregularities. However, I believe it's critical when election results are challenged that the initial critcisms be defensible. Otherwise the whole process will be needlessly discredited.
Follow the latest election news at www.twitterfall.com, select #iranelection
Benham's law has been mentioned in passing, but so far I haven't seen any analysis posted. (Benham's law quantifies the finding that the numberal 1 is generally overrepresented in data except when it is fabricated.)
Counting the digits for all four candidates in Shaahin's spreadsheet (abobe) results in the following totals:
1 906 16%
2 712 12%
3 629 11%
4 552 10%
5 535 9%
6 494 9%
7 517 9%
8 486 8%
9 477 8%
0 488 8%
All 5796 100%
"1" is indeed overepresented. I will leave it to the statisticians to confirm whether the ratio is normal.
This does not prove a legitimate election. All it suggests is that the results were not the product of a human being sitting down and writing out fabricated numbers.
Guys,
By looking at the statistics published by the Iranian Interior Ministry, We are looking at a made up data (assume the election is rigged) with random processes. It is very easy to generate a data so it can not be impossible to find out the random process behind it.
They have published the data two days after election so my guess is that it is evry hard to find out statistically significant error in it.
I've just run a simple correlation analysis on each candidate and total number of votes casted on the province. What we expect is usually very high correlations for all candidates, but for Karoubi and Rezaee it is 0.7 and 0.6. Again it is not something that based on that we can cry fraud.
Another thing is that since ahmadinejad have popularity in less populated areas I expect higher correlation between Mousavi's votes and number of casted votes than Ahmadinejad's. For Ahmadinejad, it is .987 and for Mousavi it is .963.
Guys remember that the online results again should be a better place for inconsistancies because it is given in rush.
I should also mention that there was a Fatwa by some Ayatollah which allows muslims to cheat in favor of Ahmadinejad!! This Fatwa came out a week before election.
I also should mention that one candidate's votes(Rezaee) was reduced in one wave.
I will keep looking for the inconsistancies
jackneefus, thanks for your comments. Two points:
1-The percentages you're talking about pertain to cities/counties, not to provinces. Miraculously, once you sum up these numbers for each province, Ahmadinejad's percentage doesn't change much (Would you double-check this claim please?). According to this website:
http://www.tebyan.net/politics_social/politics/domestic_policy/international/2009/5/21/92408.html
which offered a decent analysis of the previous election at that time (2005), "the most obvious voting behavior in this election was the voters' support for their local candidate [i.e. ethnic allegiance]" (my own translation). This pattern is totally absent from the 2009 election.
2-The two areas you mentioned in the province of Tehran are the city of Tehran and Shemiranat. These areas were the unbeatable strongholds of Mousavi and Karroubi. I wouldn't be surprised if 80% or more of people in these areas voted for Mousavi and Karroubi. However, the data says Mousavi just got slightly more than half of the votes in those areas. This seems utterly fishy. My theory is they just made the numbers in a way that the general fact that Tehran and Shemiranat were supporters of reformists is not violated.
Sorry, last comment had a wrong link.
I'm no statistician, but shouldn't it fit the Benford's law probability distribution? Have a look at this:
http://docs.google.com/View?id=ddcfg2mv_4g8x3c7fc
Although "1" has occured more often, the probabilities that jackneefus posted (based on the returns) does not match the formula. It looks very flattened. Doesn't that matter?
BTW: @ Horrible: Thanks for your kind comments :-).
http://www.terrorfreetomorrow.org/upimagestft/TFT%20Iran%20Survey%20Report%200609.pdf
They all know already that Ahmadinejad will win, just to create chaos in Iran
Your apparently scientific aanlysis proves nothing. Indeed the correlation could equally be used to demonstrate conscious rigging in a systematic fashion. What yo should really be comparing is the results for ast Iranian election with the current one. Using the current data for one election is the equivalent of statistical incest. Sorry, maybe you are well intentioned, but this is false science.
Love ya, Nate.
My thoughts: Such a neat fit by the "official" data may also be a result of fitting artificial data to fit expectations. If the Supreme Leader was afraid of the "Obama Effect" that took down Hamas, he would have had plenty of time to prepare cooked, statistically appropriate voting results.
His mistake, though, was releasing them immediately, instead of the typical three days later, and instigating a tyrannical shutdown of communications and freedoms.
"To properly analyze Iran's election results is probably something best left to Middle East experts, rather than experts on U.S. electoral politics."
You hit the nail on the head. People who don't know much about Iran shouldn't be pretending to know what's going on. People who work in the Mideast field and who are around Iranians know that something about these elections isn't right. Don't believe me? Ask the millions of Iranians who are risking their lives in defiance of the ban on protests right now.
@Giovanni D: Nader's 2004 voters didn't turn away from him in 2008 because all his sunshine voters (over 3/4 of all his voters) already turned away from him after they voted for him in 2000. What was left in 2004 was his core voters who would rather not vote than vote for a republicrat.
But I have no idea how this relates to Iran. I will say that I don't trust Iranian bloggers to provide a broad swath of opinions on this, given that those who have access to the internet are likely not the base of Ahmadinejad.
And I will say I don't trust vote counting in any country that uses anonymous voting. What a sham that is.
Most of the comments here miss the point. It doesn't matter how you aggregate the results, what matters is the fact that you're aggregating the results and then performing a regression-- a perfect formula for a misleadingly high correlation coefficient.
Just for fun, I randomly generated outcomes for Mousavi and Ahmadinijead for 100 districts. The results for each candidate was random and not dependent on the total for the other. No matter how ethnically fractured the Iranian electorate is, I doubt the district-level vote totals approach randomness. Next, I created a column of cumulative results and performed a regression analysis.
Guess what happened? When you sum the results, the entries are no longer independent and the result is that even though the district-level entries are completely uncorrelated (r2=0.0001), the cumulative results are super-duper correlated (similar to the Iranian data: r2=0.9955) because the entries are not independent. If anyone would like to see the data, they will be available on request in Excel or Stata format.
I am not saying the election was not rigged--I think it likely was on some level. But this is not evidence of it and Mr. Silver was right to point it out. Also--as a political scientist--I take some offense at suggestions that only an expert on the Middle East could offer any insight into whether the election was fixed. Most area studies specialists are too parochial and could only offer "impressions"-- statistics can offer real insight into voting irregularities. The only problem is that answering the question requires better data than that we are provided here.
The real issue here is that the data are internally correlated because they are running totals. This inflates R^2 artificially. I repeated the analysis using the incremental vote gains from each "wave" and found different results. The variation in the Iranian data is between 3 and 10 times less than the variation in the 2008 US presidential data. I don't think this is definitive "proof" of electoral fraud, but it is at least suspicious.
Please see:
http://thoughtrevoking.blogspot.com/2009/06/nate-silvers-analysis-of-irans-election.html
As you may know, Iran's election results are declared without mentioning province or city name (which declared after 2 days!) that means the numbers was just artificially generated.
Shaahin --
Thank you for providing the Benham's distribution. That was the missing piece.
I am not sure how aggregation affects the distribution -- I would think that would flatten the curve. So I made the same comparison on the larger 100-line breakdown you provided earlier:
http://spreadsheets.google.com/ccc?key=rJhPkQLtSRMGgZMOnbYpqBw
There is still a noticeable difference between the lines. It is possible that Benham's Law is only valid at the lowest level of data, in this case the voting place. Barring that, the data does not seem to be a natural distribution.
@ Brent: I'm very confused by your post. If I did get it right, what you did was you defined 100 districts and then groupped them together in groups of 10 or so (?) which would constitute your "provinces". Then you generated random data for the districs and summed them up for the provinces and performed a regression. Is that right?
If that's what you did, I have no idea how that proves your point. Of course you would get a high R-squared exactly because your data was random. That's exactly where Mr. Silver's analysis is flawed too. The whole point about the Iranian election returns is the district level data were NOT taken to be random. We think that if they really counted the votes, given that the first waves were announced extraordinarily early, they must have started with smaller voting districts and announced the bigger ones in the later waves. We also believe that Ahmadinejad is far more popular in smaller cities and rural areas than in urban areas. So the packets of data couldn't have been random neither on district-level nor on province-level.
It does matter how you aggregate the results after all. If you aggregate most of the pro-Ahmadinejad districts first and gradually advance to pro-Mousavi areas (what we think they must have done if they really counted the votes and given the super-early announcement of the first few waves) you will have an ascending curve which gives you a high R-squared but never nearly as high as 0.997.
Another way to put it is to compare it with the previous elections, the results were always highly sensitive to the area they belonged to even on the province-level. Look at this for example:
http://www.fivethirtyeight.com/2009/06/iran-does-have-some-fishy-numbers.html
Sorry if I got you wrong.
You might look at what TIME had to say on it's web site today:
Are Any of the Vote Totals Suspicious?By SIMON ROBINSON
Yes. Support for Ahmadinejad was strangely consistent across the country, a real change from previous elections, when candidates drew different levels of support in different regions.
There were several other puzzlers in the results:
• According to official figures, Ahmadinejad handily beat Mousavi in Mousavi's hometown of Tabriz — a shocking result, given the candidate's popularity in his own region.
• Ahmadinejad beat Mousavi in the big cities, even though Iran's very limited polling and anecdotal evidence indicate that Mousavi is far more popular than the President in cities.
• The official figures put support for the other main reformist candidate, Mehdi Karoubi, at below 1%. That is far less than what was expected, and a drastic departure from the pattern in previous elections.
I'm Iranian. Please explain how do they count 40 million votes from 10p.m. to 7 a.m.. Please be informed that the votes are handwritten and they would read manually. The employees worked 14 hours from morning until 10p.m. and as they are human they need rest and they can't count votes in midnight.
It is too easy to understand!!!!!!!!
It's interesting to see Darius has posted about explosions in Tehran even before any unrest had started!!!
Your analysis is interesting, the linear dependence between the overall votes reported over time perhaps shows how uniformly the ballots have been counted (sampled) from different regions and polling stations.
To study the temporal evolution of the reported numbers, I'd suggest devising a factor analysis model. This process (possibly combined with a PCA) can potentially point at some obvious hidden factors which can cause the two time series to be correlated, but then I am not sure how you can interpret those hidden factors for such small samples.
I see people have questioned the high turnout. This is a characteristic of our Iranian society. In Iran the number of polling stations are at least 2 or 3 times more than what I have seen in Europe, moreover people take voting as their duty. If often takes in average a couple of hours in the queues to get the chance to cast your vote.
Also, you're making another mistake! What happens in the streets of Tehran right now doesn't necessarily provide evidence that the election was rigged. Your choice of sample is again biased (contained to the people in the capital)! You don't have the slightest clue that in Iranian society how big a role class and religion can play in the choice of one's candidate. Among the lower middle class this easily goes far beyond the ethnicity, etc..
So what? It seems like the oft-quoted phrase "You can prove anything with statistics" applies here just as well..
For example, my favorite example of this is the causal relationship between global warming and the number of pirates worldwide (made famous by the followers of the gospel of the flying spaghetti monster, who posit that the power of the FSM to regulate worldwide temperatues via his noodly appendage has gone down with the decrease in the absolute numbers of his natural worshipers, the pirates..) available at:
http://is.gd/15QwB.
What you failed to do was consider the other two contestants. Include them in the mix, and you'll realize that ALL CANDIDATES' RESULTS ARE LINEAR. that means the following relationships are linear:
ahmadi-mousavi
ahmadi-karoubi
ahmadi-rezaei
mousavi-karoubi
mousavi-rezaei
karoubi-rezaei
This cannot be explained by the above article!!!
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@ Maryam: I was going to say exactly what you said: The other day, I was investigating the data for the Ahmadinejad-Karroubi, and Ahmadinejad-Rezaee graphs and I thought, how probable is it that these three happen together? Actually, of the six relationships you mention, only three are independent phenomena. Let's consider the following three:
Ahmadinejad-Mousavi (R^2=0.988)
Ahmadinejad-Karroubi (R^2=0.999)
Ahmadinejad-Rezaee (R^2=0.989)
Now, since we have three independent relationships, the probability of all three happening at the same time is the multiplication of their individual probabilities. How high the probability of each of them should be so that the joint probability is below the significant range?
x*x*x = 0.05 --> x ~ 0.37
Meaning that if each graph has an 37% or more probability of being linear, the three can happen together without being conclusive evidence of fraud. I hope everyone agrees that 37% is too high.
what do you think of the WaPo article on the ending digits of the results and their indication that they were made up by humans rather than being actual results?
http://idek.net/Fvs
Nate -
to make you comparison with the McCain/Obama contest statistically valid, you have to show that in a random partition into six "waves" of released results, the coefficient of determination has a distribution with mean close to 0.99 and small standard deviation. Otherwise we don't know if the example given by you is just a concocted extreme case.
Put differently, this is methodologically incorrect.
Hans
Re the analysis by Bernd Beber and Alexandra Scacco in the Washington Post, this is an interesting approach. One question I had as I read it, though, is whether the two phenomena they're looking at, the distribution of digits of the least significance in the disaggregated results, on on hand, and the occurrence of non-adjacent digits in the two least significant places in the same results, are properly independent.
The authors give the combined probability of what they see happening by multiplying the probability of the patterns they find for these two things together, a combined probability that is very low indeed. But isn't it necessary for the two things to be independent in order to be able to do this?
@ Hans Engler: Good point, I just want to emphasize that the results of the Iranian recent election were announced in 13 waves (on average, each consisting of about 8% of the votes). The Obama-McCain election has 3 times more votes than the recent Iranian election. Therefore a good analysis must split it up into 39 waves or so.
In other words, the less you aggregate in each wave the more the variation is expected to be. The Iranian election had three times less votes and twice as much waves.
Besides, Nate's first wave has twice as much as the other waves.
The points on the graph curve into (0,0), which implies the early results were even more strongly pro-incumbent. For example, the lowest point is about (1.5, 3.5), while the highest is about (9, 18). This is consistent with Ahmadinejad having stronger support in rural and Mousavi in urban areas. But I agree with Nate, that the lack of variation, with numbers in the millions, is not impressive. I think it is quite difficult to detect fraud purely from numbers, but the lack of checks and balances in the election process makes it easy to believe that fraud happened.
This analysis appears to be as accurate as Nate's oscar predictions.
I'm not really sure what thought process lead you to beleive that conducting the stats in this manner would be even remotely accurate in predicting variance.
Counting started in rural areas and smaller districts which were assumed to be pro-Ahmadinezhad and pro government media have always claimed this. Large cities and Tehran which were more pro-Mousawi were counted in the latest wave. That is the reason why a non-linear correlation would be expected. By the way there are tens of other pieces of evidence that this was a fraudulent election.Keep googling.
For those of you who claim that the election results were declared "too quickly" and that it was supposedly "impossible" for the handwritten votes to be counted so fast, the fact is that there were 47000 counting stations, with an average of about 800 votes to be counted per station. Easily done in a short time. See IranAffairs.com for the debunking of other Iran election fraud claims.
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By comparing the traditional Internet users, Internet users to iResearch found that the traditional white-collar-based, cell phones wholesale, corporate general staff accounted for 18.9%, higher than the 5.6% of the wholesale cell phones users accounting; and discount cell phones users in the years students and blue-collar workers accounted for significantly more than the traditional Internet users, respectively, accounting for 19.5% and 18.9%, higher than the traditional Internet users Students and blue-collar workers accounted for 7.8% and 5.1% respectively.
From cell phones users to see the specific situation of occupational segmentation in 2009, accounting for 19.5% of students dropped 21.2 percent over last year, other types of occupations than those last year, the proportion of Internet users cheap cell phones increase. White collar crowd from last year's 29.2% increase to 38.9% this year, accounting for 9.7 percentage points up to replace the student groups cellphone users as one of the biggest occupational hierarchy; blue-collar crowd from last year's 13.9% to 18.9% this year, accounting for rose by 5.0 percentage points, showing that mobile phones users by a group of students to the occupational groups a significant trend in the development. Ereli advice that, cheap cell phones and mobile phone users Internet users monthly income distribution of age, education, occupational distribution has strong correlation with high spending capacity of white-collar workers and some students in the crowd will be a huge cell phone china online potential consumer groups.
The survey found that consumer 3G wholesale china from the crowd of view, the buyer 25 to 40 years old mainly white-collar workers, accounting for about 40%, followed by consumer groups of students, accounting for about three into. According to statistics, 3G wholesale products in sales, compared with a 2G mobile phone sales are still a wide gap between, but since June has been, 3G mobile phones increase in the average monthly buy products for more than 50%, "11" period due to holiday business, the increase of more than 150%. Pk that the "11" after the peak sales of 3G handsets likely to usher in more stable growth.
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