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Anatoly_Vorobey comments on Open thread, 9-15 June 2014 - Less Wrong Discussion
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Here's an interesting application of elementary probability theory.
Syria recently held an election, in the midst of a civil war. Dr. Bashar Hafez al-Assad wins post of President of Syria with sweeping majority of votes at 88.7%.
The elections were a sham. The vote counts are completely fraudulent. And you can learn this just from the results page linked above, without knowing anything about Syria or its internal politics. How?
The results are too accurate.
"11,634,412 valid ballots, Assad wins with 10,319,723 votes at 88.7%". That's not 88.7%, that's 88.699996%. Or in other words, that's 88.7% of 11,634,412, which is 10,319,723.444, rounded to a whole person.
The same is true about all other percentages in this election. In one of the results there's even a bad rounding error: 4.3% cast for Al-Nouri is 11,634,412 * 0.043 = 500,279.716 votes which is rounded down to 500,279 votes in the results instead of the closer 500,280. As a result, the total number of all alternatives (three candidates + incorrect ballots) differs from the total number of valid ballots by 1 (442,108 + 10,319,723 + 500,279 + 372,301 = 11,634,411 and not 11,634,412. If they were rounding correctly, their fake numbers would've looked better. In either case, it's evident that someone took the total vote count, calculated the percentages and rounded.
(why is this an application of elementary probability theory? You can calculate the probability of such an exact percentage of votes occurring by chance).
(to the best of my knowledge, this was first noted in this Russian-language Facebook post. Recently there had been an identical case with a sham referendum in a Ukrainian province controlled by separatists, which is what got people interested in looking at vote counts).
I have no idea how likely it is, but an alternative explanation is that the vote counts were first converted to percentages to one decimal place, then someone else converted them back to absolute numbers for this announcement.
Nice work. I tend to take high-profile election results over 66% or so in favor of one option as prima facie evidence of election fraud (maybe 75 if there's some exceptionally strong reason to vote one way or another, like if one of the candidates is dead), but this is certainly damning.
You'd think that the perpetrators of electoral fraud would realize this sort of thing -- but I suppose the most likely explanation is that (dons Robin Hanson glasses) elections in these cases aren't about legitimacy, but rather about proving that one party has enough power to enforce a clearly illegitimate result.
Referenda on things like secession or constitutional change tend to have extreme landslide victories or defeats, even ones generally agreed to have been fair.
http://en.wikipedia.org/wiki/Independence_referendum
Lots of these are in the 80s and 90s.
Very nice! I love this kind of mathematical detective-story - I'm reminded of Nate Silver's consideration of the polling firm Strategic Vision here and here - but this is far, far more blatant.