

A Mathematical Analysis Of The Iranian Elections - avner
http://www.washingtonpost.com/wp-dyn/content/article/2009/06/20/AR2009062000004.html?referrer=reddit

======
larryfreeman
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
> 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.

~~~
smanek
Go read up on Benford's law. (See
[http://www.journalofaccountancy.com/Issues/1999/May/nigrini....](http://www.journalofaccountancy.com/Issues/1999/May/nigrini.htm)
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.

------
jimfl
Weird. The article is invoking Benford's Law without identifying it.

<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-
ele...](http://www.jgc.org/blog/2009/06/benfords-law-and-iranian-
election.html)

~~~
jules
The article is about the last digits of the numbers. Benfords law is about the
first digits.

~~~
jimfl
[http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_...](http://en.wikipedia.org/wiki/Benford%27s_law#Generalization_to_digits_beyond_the_first)

~~~
jules
Right, that's why I said digits. The law pretty much says "uniform" for the
last digits, like this article.

------
WilliamLP
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
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
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.

------
Dilpil
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
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.pn...](http://img.skitch.com/20090621-xrmw8yrxaec15jku414ffb2cjq.png)
-or- <http://earlh.com/HN/iran.R> , and <http://earlh.com/HN/Iran_2009.csv>

Here's a histogram:
[http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.pn...](http://img.skitch.com/20090621-ewdbtr9q2cw5hyemn64fg3kbqd.png)

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.pn...](http://img.skitch.com/20090621-dx6nqws4u9rc5p3nghsnuy24j3.png)

\--------- 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
<http://news.ycombinator.com/formatdoc>

~~~
earl
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)

------
ars
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
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.

------
TweedHeads
"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
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.

