6 ms·

A Mathematical Analysis Of The Iranian Elections

25 points by avner 17y ago

WilliamLP 17y ago
The real question is: given any set of data, after the fact, what is the chance that a numerology detective can find some metric that will indicate suspicious activity? (Pretty much 100%) I'm calling bullshit.
- earl 17y ago
  It's not unreasonable to expect that the last two digits of the voting counts should be distributed uniformly. Given that we also know that the wiring in human brains keeps us from properly sampling a uniform distribution by hand, the article employed a simple strategy of looking at the last two digits, assuming they were drawn from a uniform distribution, and asking if that were so, what is the probability that this would be our draw? You gave no reason to be skeptical, and simply illustrated your lack of familiarity with basic tools of probability. Funny that you would below speak of a "stunning example [...] of mathematical ignorance." If you wanted to substantively contribute to the discussion, perhaps you should try explaining why this was an invalid test instead of just labeling the authors as "numerology detectives?"
  - bilbo0s 17y ago
    To be fair. It should be noted that US and UK elections have far larger variances than the elections in Iran. I suspect it is because incumbent politicians are allowed to engage in 're-districting'. I would need more data to make a definitive statement on the 'why'. In my view though, when Republicans carve out new districts in Mississippi and Louisiana, and when Democrats carve out new districts in Chicago, it is a form of election tampering. A very effective form of election tampering. Only the evidence of having tampered with the elections via re-districting shows up via Benford's law. Again, that part is just a theory. The explanation could be as simple as tamperers stuffing ballot boxes in the US as well.
  - kvh 17y ago
    I think his point is that if a hundred such political scientists used a hundred different methods of evaluating election results, one of them would be guaranteed to find evidence of fraud. the other 99 would not report there results, not having found anything exciting. im not convinced there ARE that many tests you could perform, but the general point is interesting...
- itistoday 17y ago
  Calling bullshit on your own post might be a smarter idea. Just because it's not intuitive to you doesn't mean it's not mathematically sound. Your post amounts to "I don't understand statistics or what the hell this article is talking about, therefore I'm going to be suspicious of it."
  - scscsc 17y ago
    Negative. It is intuitive (and wrong). It is not mathematically sound. He does understand statistics. The point he's making is that the author of the article chose the metrics after the act. There are tons of such metrics to use; if you are not honest, you can search for the ones that prove your point.
  - WilliamLP 17y ago
    It's not that difficult an idea, even if the trend of comment voting here indicates a disturbing ignorance of how statistics can be manipulated. What would be mathematically sound would be to agree on a standard set of tests, perhaps including Benford's law, digit distribution, two digit combinations shown to be popular when humans pick numbers at random. And to do so _BEFORE THE DATA HAVE BEEN AVAILABLE_. How would I trick people into believing a false conclusion? One way would be to find 30 or so measures of what could suggest suspicious patterns. Then I'd test the data with them, and perhaps there would be 2 which have a 5% chance of occurring purely by chance. Then I say "Aha! Look at this! The chance of these two things happening are .05 * 0.05 or practically impossible!" Apparently I could fool some pretty smart people this way, since they obviously aren't immune to basic statistical fallacy. As another poster said, none of this suggests that the data weren't manipulated, but just that the stats in the article, as given, are purely bullshit.
    - kvh 17y ago
      For instance, the same authors, in a previous paper analyzing nigerian election results, state the following "lab experiments indicate that individuals tend to favor small numbers, even when subjects have incentives to properly randomize. Second, individuals underestimate the likelihood of digit repetition in sequences of random integers, so we should observe relatively fewer instances of repeated numbers in manipulated vote tallies." there is no mention of either of these statistics in the Iran analysis.
TweedHeads 17y ago
"It's not the people who vote that count. It's the people who count the votes." (Josef Stalin) Either if the elections are rigged or not, 49% of the population can not be subdued to the will of the ruling 51% We need to change electoral systems, specially "winner takes all" ideologies, the tyranny of the majority. We need to learn to live together and share power together. And to separate if we can not. Nothing should be imposed.
- quizbiz 17y ago
  I think calling electoral systems, a tyranny of the majority, is a gross exaggeration. A multiparty system, one with an empowered opposition where bills require 2/3s not merely 1/2, encourages this within an electoral system. In Iran, trust in the system was lost. This is much about Iran's supreme leader as it is about the election for president.
- bilbo0s 17y ago
  This is the first sensible statement on political systems I have heard in a long time. You are absolutely correct, the problem in Iran is not a lack of democracy, it is tyranny through democratic means. Just because you win an election, does that mean you should be able to do something that the other 49% of the people find intolerable? It depends on whether you believe in democracy as a guiding principle, or in democracy as the letter of the law. The belief in democracy as the letter of the law, is, in my opinion, democracy taken to the extreme. It is the definition proffered by those who would use democracy as a cover for wanting, winning, and wielding power over those who may, legitimately, disagree with them. Democracy is a beautiful idea. Now, thanks to the efforts of politicians in democracies of all stripes, not just those in Iran, it has become the principle endorser of divisiveness in the world of ideas. It is being used to give violently divisive ideas an air of legitimacy that they do not deserve.
- mixmax 17y ago
  In Denmark we have a multi party system, and the government is a coalition of the parties that are represented in parlaiment. Often the government is a minority government and relies upon one or more of the other parties to get laws passed. Sometimes coalitions with similar interests appear, and as long as they have a majority they can pass laws. This system has the advantage that minority views are not only heard but also have votes. And since politics is a game of agreements, coalitions and I'll scratch your back if you scratch mine even small parties have a chance of getting legislation passed if they are willing to compromise on something else. It equates to more consensus seeking legislation, and an often vocal minority that actually has political influence.
jimfl 17y ago
Weird. The article is invoking Benford's Law without identifying it. http://en.wikipedia.org/wiki/Benford%27s_law http://en.wikipedia.org/wiki/Benford%27s_law Here's an article that concludes that the election results do not run afoul of Benford's Law: http://www.jgc.org/blog/2009/06/benfords-law-and-iranian-election.html http://www.jgc.org/blog/2009/06/benfords-law-and-iranian-ele...
- jimfl 17y ago
  And an even more in-depth analysis [PDF]: http://arxiv.org/pdf/0906.2789 http://arxiv.org/pdf/0906.2789
  - itistoday 17y ago
    Would anyone be so kind as to translate that into plain English?
- jules 17y ago
  The article is about the last digits of the numbers. Benfords law is about the first digits.
  - jimfl 17y ago
    http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_to_digits_beyond_the_first http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_...
    - jules 17y ago
      Right, that's why I said digits. The law pretty much says "uniform" for the last digits, like this article.
larryfreeman 17y ago
The article is very interesting in my view. It states that a sampling of the numbers do not follow expected random patterns. But let's talk about the real issue. When you forbid independent monitors, announce results before the votes gets counted, and conclude absolute certainty in the results before there is a statistical analysis, it is hard to believe in a fair election.
- WilliamLP 17y ago
  > The article is very interesting in my view. It states that a sampling of the numbers do not follow expected random patterns. If you try a whole bunch of fairly arbitrary metrics, e.g. how many end in 7, how many end in 5, how many have consecutive increasing digits, and you mine the data into finding two arbitrary ones that random chance would say occur 5% of the time, does that really tell you anything about the data? I find this article a stunning example of the dangers of mathematical ignorance.
  - deleted 17y ago
    [deleted]
  - scscsc 17y ago
    I don't get why you are modded down. Mathematically, the article is a piece of junk (which doesn't mean the elections were fair -- I don't think there's anyone in the democratic parts of Earth who thinks they were fair). You are of course right, why choose exactly those two metrics? Also, the two metrics are probably not independent, so taking their product is bogus. The article was written by a 'PhD candidate' in political sciences. I think he should get his degree. He learned how to convincingly misuse statistics.
  - smanek 17y ago
    Go read up on Benford's law. (See http://www.journalofaccountancy.com/Issues/1999/May/nigrini.htm http://www.journalofaccountancy.com/Issues/1999/May/nigrini.... for an example of how it was used) I'm not familiar with the digit-distribution law the article mentioned, but on its face it doesn't seem entirely unreasonable. I'd prefer to see some study applying this same analysis to thousands of other elections, of course. But, prima facie, using digit distributions to detect fraud is not at all unreasonable.
ars 17y ago
Again, people fall into the fallacy that statistical averages must be followed exactly. It is not so. Edit: Very surprised at the -3 mod. Are people here really so bad at statistics that they think this? Example: Just because the average rainfall in a spot is 10 inches, does NOT mean it has to be 10 inches every year. If you have 6 inches one year that is NOT an anomaly. That is perfectly normal. Sure it might be unlikely - but unlikely things still happen! In fact they must happen, just not as often at the more likely things. So the analysis of the votes, sure it might not match the average, but that doesn't mean a whole lot. It could simply mean that you happened to get the 10% chance. PS. Not that the vote fraud is in question. It's not, it's obviously fake. But not because of this analysis.
- pmjordan 17y ago
  A lot of scientists would be very pleased to have results with a 99.5% confidence. The fact that the results have a 0.5% chance of being real, combined with the fact that Ahmadinejad's votes have a significantly different distribution from the other candidates' makes this a pretty strong argument.
- robryan 17y ago
  He wasn't claiming though that it defiantly pointed to the election being rigged, just pointing out the statistic likelihood based on that method.
Dilpil 17y ago
Is there a link to a more technical version of this somewhere? That might settle alot of the debates going on (on this website that is).
- earl 17y ago
  You can go straight to their website, but here is an alternate analysis. My apologies for not having time to do both their analyses, I'll try when I get home, but I have to run. Grab their data: Iran_2009.csv Then: (apparently I can't embed preformatted text. Sorry.) Try this: http://img.skitch.com/20090621-xrmw8yrxaec15jku414ffb2cjq.png http://img.skitch.com/20090621-xrmw8yrxaec15jku414ffb2cjq.pn... -or- http://earlh.com/HN/iran.R http://earlh.com/HN/iran.R , and http://earlh.com/HN/Iran_2009.csv http://earlh.com/HN/Iran_2009.csv Here's a histogram: http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.png http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.pn... The p-value I get is p-value = 0.07685 NB: there is something weird going on with their data: it doesn't sum properly. http://img.skitch.com/20090621-dx6nqws4u9rc5p3nghsnuy24j3.png http://img.skitch.com/20090621-dx6nqws4u9rc5p3nghsnuy24j3.pn... --------- So, the way this works is that I look at the last digit in each of the totals, then ask what is the probability that we should observe such a distribution of final digits if the final digit were distributed as discrete uniform U[0,9]. I use a chi2 goodness of fit test, then calculate the p-value with H0 = the final digits are distributed uniformly. We would reject H0 and say the election was rigged at an alpha level of 0.9, but not at 0.95. Take of this what you will, but I'd hope to have a higher significance level for elections. : shrug :
  - mattyb 17y ago
    http://news.ycombinator.com/formatdoc http://news.ycombinator.com/formatdoc
    - earl 17y ago
      Oh thanks! I suck for missing that... Code for above: d <- read.csv(file='~/stuff/earlh/Iran_2009.csv', header=T, sep=',') lastDigit <- function(v){ v - 10*floor(v/10) } digits <- lastDigit( c(d$Ahmadinejad, d$Karroubi, d$Mousavi, d$Rezaee)) hist(digits, breaks=10) #chi2 gof tab <- table(digits) n <- length(digits) model <- chisq.test(x=tab, p=rep(0.1, 10)) model # hand generated -- check our work above ts <- 0 for(i in 1:length(tab)){ ts <- ts + ( tab[[i]] - 0.1*n)^2 / (0.1*n) } qchisq(p=1-0.076, df=9)
deleted 17y ago
[deleted]

25 points by avner 17y ago

The real question is: given any set of data, after the fact, what is the chance that a numerology detective can find some metric that will indicate suspicious activity? (Pretty much 100%) I'm calling bullshit.

earl 17y ago
It's not unreasonable to expect that the last two digits of the voting counts should be distributed uniformly. Given that we also know that the wiring in human brains keeps us from properly sampling a uniform distribution by hand, the article employed a simple strategy of looking at the last two digits, assuming they were drawn from a uniform distribution, and asking if that were so, what is the probability that this would be our draw? You gave no reason to be skeptical, and simply illustrated your lack of familiarity with basic tools of probability. Funny that you would below speak of a "stunning example [...] of mathematical ignorance." If you wanted to substantively contribute to the discussion, perhaps you should try explaining why this was an invalid test instead of just labeling the authors as "numerology detectives?"
- bilbo0s 17y ago
  To be fair. It should be noted that US and UK elections have far larger variances than the elections in Iran. I suspect it is because incumbent politicians are allowed to engage in 're-districting'. I would need more data to make a definitive statement on the 'why'. In my view though, when Republicans carve out new districts in Mississippi and Louisiana, and when Democrats carve out new districts in Chicago, it is a form of election tampering. A very effective form of election tampering. Only the evidence of having tampered with the elections via re-districting shows up via Benford's law. Again, that part is just a theory. The explanation could be as simple as tamperers stuffing ballot boxes in the US as well.
- kvh 17y ago
  I think his point is that if a hundred such political scientists used a hundred different methods of evaluating election results, one of them would be guaranteed to find evidence of fraud. the other 99 would not report there results, not having found anything exciting. im not convinced there ARE that many tests you could perform, but the general point is interesting...
itistoday 17y ago
Calling bullshit on your own post might be a smarter idea. Just because it's not intuitive to you doesn't mean it's not mathematically sound. Your post amounts to "I don't understand statistics or what the hell this article is talking about, therefore I'm going to be suspicious of it."
- scscsc 17y ago
  Negative. It is intuitive (and wrong). It is not mathematically sound. He does understand statistics. The point he's making is that the author of the article chose the metrics after the act. There are tons of such metrics to use; if you are not honest, you can search for the ones that prove your point.
- WilliamLP 17y ago
  It's not that difficult an idea, even if the trend of comment voting here indicates a disturbing ignorance of how statistics can be manipulated. What would be mathematically sound would be to agree on a standard set of tests, perhaps including Benford's law, digit distribution, two digit combinations shown to be popular when humans pick numbers at random. And to do so _BEFORE THE DATA HAVE BEEN AVAILABLE_. How would I trick people into believing a false conclusion? One way would be to find 30 or so measures of what could suggest suspicious patterns. Then I'd test the data with them, and perhaps there would be 2 which have a 5% chance of occurring purely by chance. Then I say "Aha! Look at this! The chance of these two things happening are .05 * 0.05 or practically impossible!" Apparently I could fool some pretty smart people this way, since they obviously aren't immune to basic statistical fallacy. As another poster said, none of this suggests that the data weren't manipulated, but just that the stats in the article, as given, are purely bullshit.
  - kvh 17y ago
    For instance, the same authors, in a previous paper analyzing nigerian election results, state the following "lab experiments indicate that individuals tend to favor small numbers, even when subjects have incentives to properly randomize. Second, individuals underestimate the likelihood of digit repetition in sequences of random integers, so we should observe relatively fewer instances of repeated numbers in manipulated vote tallies." there is no mention of either of these statistics in the Iran analysis.

TweedHeads 17y ago

"It's not the people who vote that count. It's the people who count the votes." (Josef Stalin) Either if the elections are rigged or not, 49% of the population can not be subdued to the will of the ruling 51% We need to change electoral systems, specially "winner takes all" ideologies, the tyranny of the majority. We need to learn to live together and share power together. And to separate if we can not. Nothing should be imposed.

quizbiz 17y ago
I think calling electoral systems, a tyranny of the majority, is a gross exaggeration. A multiparty system, one with an empowered opposition where bills require 2/3s not merely 1/2, encourages this within an electoral system. In Iran, trust in the system was lost. This is much about Iran's supreme leader as it is about the election for president.
bilbo0s 17y ago
This is the first sensible statement on political systems I have heard in a long time. You are absolutely correct, the problem in Iran is not a lack of democracy, it is tyranny through democratic means. Just because you win an election, does that mean you should be able to do something that the other 49% of the people find intolerable? It depends on whether you believe in democracy as a guiding principle, or in democracy as the letter of the law. The belief in democracy as the letter of the law, is, in my opinion, democracy taken to the extreme. It is the definition proffered by those who would use democracy as a cover for wanting, winning, and wielding power over those who may, legitimately, disagree with them. Democracy is a beautiful idea. Now, thanks to the efforts of politicians in democracies of all stripes, not just those in Iran, it has become the principle endorser of divisiveness in the world of ideas. It is being used to give violently divisive ideas an air of legitimacy that they do not deserve.
mixmax 17y ago
In Denmark we have a multi party system, and the government is a coalition of the parties that are represented in parlaiment. Often the government is a minority government and relies upon one or more of the other parties to get laws passed. Sometimes coalitions with similar interests appear, and as long as they have a majority they can pass laws. This system has the advantage that minority views are not only heard but also have votes. And since politics is a game of agreements, coalitions and I'll scratch your back if you scratch mine even small parties have a chance of getting legislation passed if they are willing to compromise on something else. It equates to more consensus seeking legislation, and an often vocal minority that actually has political influence.

jimfl 17y ago

Weird. The article is invoking Benford's Law without identifying it. http://en.wikipedia.org/wiki/Benford%27s_law http://en.wikipedia.org/wiki/Benford%27s_law Here's an article that concludes that the election results do not run afoul of Benford's Law: http://www.jgc.org/blog/2009/06/benfords-law-and-iranian-election.html http://www.jgc.org/blog/2009/06/benfords-law-and-iranian-ele...

jimfl 17y ago
And an even more in-depth analysis [PDF]: http://arxiv.org/pdf/0906.2789 http://arxiv.org/pdf/0906.2789
- itistoday 17y ago
  Would anyone be so kind as to translate that into plain English?
jules 17y ago
The article is about the last digits of the numbers. Benfords law is about the first digits.
- jimfl 17y ago
  http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_to_digits_beyond_the_first http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_...
  - jules 17y ago
    Right, that's why I said digits. The law pretty much says "uniform" for the last digits, like this article.

larryfreeman 17y ago

The article is very interesting in my view. It states that a sampling of the numbers do not follow expected random patterns. But let's talk about the real issue. When you forbid independent monitors, announce results before the votes gets counted, and conclude absolute certainty in the results before there is a statistical analysis, it is hard to believe in a fair election.

WilliamLP 17y ago
> The article is very interesting in my view. It states that a sampling of the numbers do not follow expected random patterns. If you try a whole bunch of fairly arbitrary metrics, e.g. how many end in 7, how many end in 5, how many have consecutive increasing digits, and you mine the data into finding two arbitrary ones that random chance would say occur 5% of the time, does that really tell you anything about the data? I find this article a stunning example of the dangers of mathematical ignorance.
- deleted 17y ago
  [deleted]
- scscsc 17y ago
  I don't get why you are modded down. Mathematically, the article is a piece of junk (which doesn't mean the elections were fair -- I don't think there's anyone in the democratic parts of Earth who thinks they were fair). You are of course right, why choose exactly those two metrics? Also, the two metrics are probably not independent, so taking their product is bogus. The article was written by a 'PhD candidate' in political sciences. I think he should get his degree. He learned how to convincingly misuse statistics.
- smanek 17y ago
  Go read up on Benford's law. (See http://www.journalofaccountancy.com/Issues/1999/May/nigrini.htm http://www.journalofaccountancy.com/Issues/1999/May/nigrini.... for an example of how it was used) I'm not familiar with the digit-distribution law the article mentioned, but on its face it doesn't seem entirely unreasonable. I'd prefer to see some study applying this same analysis to thousands of other elections, of course. But, prima facie, using digit distributions to detect fraud is not at all unreasonable.

ars 17y ago

Again, people fall into the fallacy that statistical averages must be followed exactly. It is not so. Edit: Very surprised at the -3 mod. Are people here really so bad at statistics that they think this? Example: Just because the average rainfall in a spot is 10 inches, does NOT mean it has to be 10 inches every year. If you have 6 inches one year that is NOT an anomaly. That is perfectly normal. Sure it might be unlikely - but unlikely things still happen! In fact they must happen, just not as often at the more likely things. So the analysis of the votes, sure it might not match the average, but that doesn't mean a whole lot. It could simply mean that you happened to get the 10% chance. PS. Not that the vote fraud is in question. It's not, it's obviously fake. But not because of this analysis.

pmjordan 17y ago
A lot of scientists would be very pleased to have results with a 99.5% confidence. The fact that the results have a 0.5% chance of being real, combined with the fact that Ahmadinejad's votes have a significantly different distribution from the other candidates' makes this a pretty strong argument.
robryan 17y ago
He wasn't claiming though that it defiantly pointed to the election being rigged, just pointing out the statistic likelihood based on that method.

Dilpil 17y ago

Is there a link to a more technical version of this somewhere? That might settle alot of the debates going on (on this website that is).

earl 17y ago
You can go straight to their website, but here is an alternate analysis. My apologies for not having time to do both their analyses, I'll try when I get home, but I have to run. Grab their data: Iran_2009.csv Then: (apparently I can't embed preformatted text. Sorry.) Try this: http://img.skitch.com/20090621-xrmw8yrxaec15jku414ffb2cjq.png http://img.skitch.com/20090621-xrmw8yrxaec15jku414ffb2cjq.pn... -or- http://earlh.com/HN/iran.R http://earlh.com/HN/iran.R , and http://earlh.com/HN/Iran_2009.csv http://earlh.com/HN/Iran_2009.csv Here's a histogram: http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.png http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.pn... The p-value I get is p-value = 0.07685 NB: there is something weird going on with their data: it doesn't sum properly. http://img.skitch.com/20090621-dx6nqws4u9rc5p3nghsnuy24j3.png http://img.skitch.com/20090621-dx6nqws4u9rc5p3nghsnuy24j3.pn... --------- So, the way this works is that I look at the last digit in each of the totals, then ask what is the probability that we should observe such a distribution of final digits if the final digit were distributed as discrete uniform U[0,9]. I use a chi2 goodness of fit test, then calculate the p-value with H0 = the final digits are distributed uniformly. We would reject H0 and say the election was rigged at an alpha level of 0.9, but not at 0.95. Take of this what you will, but I'd hope to have a higher significance level for elections. : shrug :
- mattyb 17y ago
  http://news.ycombinator.com/formatdoc http://news.ycombinator.com/formatdoc
  - earl 17y ago
    Oh thanks! I suck for missing that... Code for above: d <- read.csv(file='~/stuff/earlh/Iran_2009.csv', header=T, sep=',') lastDigit <- function(v){ v - 10*floor(v/10) } digits <- lastDigit( c(d$Ahmadinejad, d$Karroubi, d$Mousavi, d$Rezaee)) hist(digits, breaks=10) #chi2 gof tab <- table(digits) n <- length(digits) model <- chisq.test(x=tab, p=rep(0.1, 10)) model # hand generated -- check our work above ts <- 0 for(i in 1:length(tab)){ ts <- ts + ( tab[[i]] - 0.1*n)^2 / (0.1*n) } qchisq(p=1-0.076, df=9)

deleted 17y ago

[deleted]