## The Syrian p-value that I didn’t bother to calculate

I posted something on the sister blog about the fake vote totals from the Syrian election. We know the numbers are fake from the official report, which reads:

Speaker of the People’s Assembly, Mohammad Jihad al-Laham announced Wednesday that Dr. Bashar Hafez al-Assad won the post of the Syrian Arab Republic’s President for a new constitutional term . . . The number of those who have the right to take part in the presidential elections inside and outside Syria reached at 15.845.575 citizens and the number of participants in the voting reached at 11.634.412 while the number of invalid papers reached at 442.108 with 3.8%.

He added that the number of votes each candidate has gained in a proper sequence was: Dr. Bashar Hafez al-Assad is 10.319.723 votes with 88.7% out of the correct votes, Dr. Hassan Abdullah al-Nouri, got 500,279 votes with a percentage of 4.3% of the valid votes, while Mr. Maher Abdul-Hafiz Hajjar got 372,301 with a percentage of 3.2% of the valid votes.

Speaker al-Laham said that the announcement of results came in accordance with article No. 86 of the Constitution and item B of Article 79 of the General Elections’ Law, expressing, by the name of People’s Assembly, his pride of the Syrian people’s option and their correct decision, blessing, at the same time, this Arab leader who is confident in his people’s will.

OK, I just included the last paragraph for its amusement value. As was pointed out to me by Anatoly Vorobey, the real clues are in the earlier paragraphs. The trouble is that those percentages are exact. Here are the numbers:

Assad: 0.887 * 11634412 = 10319723.4
Nouri: 0.043 * 11634412 = 500279.7
Hajjar: 0.032 * 11634412 = 372301.2
Invalid ballots: 0.038 * 11634412 = 442107.7

In each case, the reported vote total is a rounded version of the exact percentage (even, oddly enough, the reported number of invalid ballots). What’s the probability of this happening? The exact percentages are 0.001*11634412 = 11634 votes apart. Each exact percentage could come to two different reported votes (as you could round up or down), thus the chance of accidentally hitting an exact percentage is 1 in 11634/2=5817. The probability of this happening 4 times, completely by chance, is 1/5817 to the 4th power, or 8.7 x 10^-16. [Correction: as Bob pointed out in comments, the 4 numbers are constrained to add to the total, so the exact match is only happening 3 independent times, which gives a p-value of approximately 1/5817 to the 4th power, or 5 x 10^-12.]

So that’s the p-value. But I couldn’t bring myself to compute it. It’s such an extreme number, it’s just silly. Enough to say that the evidence is clear.

On the other hand, if I had written it up as an article, computed the p-value, and put it on Arxiv, maybe it would’ve gotten some attention—maybe even blogged at the Washington Post . . .

No longer riding on the merry-go-round,
I just had to let it go.

1. Bob says:

Hmm. Are you sure that “The probability of this happening 4 times, completely by chance, is 1/5817 to the 4th power, or 8.7 x 10^-16.” ?

Given that the four percentages total to 100%, wouldn’t it be the case that if 3 of the vote numbers were very close to multiples of 11634, that the fourth would be also? So, the outcome is not so improbable—probably something like (1/5817)^3.

There is another possibility. The numbers were prepared honestly. But, the guy doing the press release only had the total and the (honest) percentages. So, he solved for the approximate votes and put those numbers in the announcement.

Bob

• Andrew says:

Bob:

1. Good point; I corrected the post accordingly.

2. Yes, I mentioned that exact possibility in my linked post. It is possible that the fake vote totals were the product of innumeracy and poor communication rather than fraud. I’ll have to say, though, that it doesn’t look good when the numbers in the official report are wrong.

• germo says:

Wouldn’t the probability be even lower than (1/5817)^3? Clearly the numbers are not independent and so chain rule of probability should be applied?

People say I’m crazy/ blogging my life away…
(sorry)

3. olga says:

They always report raw counts and round the percentages. Hence percentage*total is not equal the raw count and should not be equal to the raw number. Am I missing something? The problem is that percentage is not of the valid votes (as they say) but of the total votes but that may be the translation problem.

• Andrew says:

Olga:

The problem is that the reported raw counts are clearly not raw counts. The percentages are too exact for that to be realistically possible.

4. Jonathan Gilligan says:

Umm. Speaking to Bob’s final point, we know a lot from other sources about the general honesty of the Syrian government, so a good exercise for the reader would be to re-analyze these numbers, taking our prior knowledge into account.

5. Robin Morris says:

Damn, I thought that this was at least one place where we could get away from it.
(which posted to the piazza course page by one of the students:)

6. JD says:

I am probably just confused, but I only calculate *one* of the vote totals as yielding an “exact” 1/10th of a percentage, 10319723/11634412=.887.

This is not to say that I think the vote totals are any more reliable.

7. Rahul says:

Are there similar vote totals & percents published for US , UK etc? Might be fun to compare. And to see how often we do have a serindipitous proper percent.

8. wei says:

so here we see again the problem of p-value: it only measures the deviation from null, and it does not contrast the null against certain alternative hypotheses. we are looking forward to some bayes factor calculations.