US elections are as 'non-normal' as Russian elections

Author: Mikhail Simkin

Last month I discussed the allegation that the results of Russian parliamentary elections violate mathematics. The figure below shows the distribution of the percent of the vote for parties among election precincts. It travelled over hundreds of blogs during past couple of weeks and was accompanied by comments that the distribution for the United Russia party violates a fundamental law of nature because it is non-Gaussian. In that previous article I argued that there is no reason for the distribution to be Gaussian, however, a commentator challenged me to show non-Gaussian distributions in US elections and so I took up the challenge.

Figure 1.  The distribution of the percent of the vote for parties among election precincts. The x-axis shows percentage of votes for the party, y-axis – number of precincts. The bin is 0.5%. Brown line is for United Russia, red – Communist party, green - Russian United Democratic Party

I decided to look at 2008 Republican primaries mainly because this was the last election I voted in. The primaries differ from national elections because different states hold their vote on different dates. Some candidates drop out during the race and it complicates the analysis. However, 21 states held elections the same day, called Super Tuesday. Since almost half of the nation votes the same day it looks like a National primary. The most complete elections results database I could find is Dave Leip's Atlas of U.S. Presidential Elections (http://uselectionatlas.org/). It does not have precinct level results for the election in question but has results by county for 19 out of 21 Super Tuesday states (except for Alaska and North Dakota). I computed the distribution of the percent of the vote for four major candidates among 1,162 counties. See Table 1 and Figure 2.

Map of the Republican Party (United States) presidential primaries, 2008

Map of the Republican Party (United States)

presidential primaries in 2008.

Green: McCain; Yellow: Romney

and Blue: Huckabee.

Image by Applysense/Wikimedia.

As you can see in Figure 1, the Huckabee distribution has two equal peaks at 15 and 35 percent. The drop between peaks is half the peak’s height. The McCain distribution has one peak at 35% and another at 80%. Between these peaks, the distribution drops almost to zero. Romney has one peak at 25% and another at 90%. Paul got an exponential distribution which resembles the one of “Yabloko” in Russian elections. There is little Gaussian about these distributions. Apparently, American elections also “violate Gauss’s groundbreaking work on statistics.”

Another issue brought to light by bloggers is that there are some spurious peaks at 50% and other multiples of 10 (see Figure 1). However, when you go to precinct-level results – you notice that in many precincts very few people voted, as little as 1 in some of them. When 2, 4, 6, 8, or 10 people voted you can get a 50% result, but never a 49% result. Can it explain it all? I plan to address this question in a future article.

Table 1.  Results of 2008 Republican presidential primaries in 19 Super Tuesday states. Figure 2 shows the same data graphically.

Figure 2. The distribution of the percent of the vote for four major candidates among 1,162 counties.

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KR

No offense to the author intended but Republican primaries 2008 may not be the best example of fraud-free elections. The analysis actually suggests that there was vote tampering in favor of both Romney and McCain. (http://www.themoneyparty.org/main/wp-content/uploads/2012/10/2008_2012_ElectionsResultsAnomaliesAndAnalysis_V1.51.pdf). It will not necessary affect the shape of distributions but you may want to look into it.

reply to this comment

B

Could the peak that McCain has at 80% be votes from his home state of Arizona?  It seems like the fact that people tend to vote for guys from their home state would very easily explain why these American politicians have small peaks at the upper end of the scale.

reply to this comment

bbzippo

The data from KOIBs (electronic ballot boxes) does look interesting:

http://bbzippo.wordpress.com/2012/01/19/russian-elections-electronic-ballot-boxes/

reply to this comment

bbzippo

Additionally, see one typical example of "ethnic diversity", "social contrasts" and so forth. 

Two neighbor precincts in the Moscow city, Ramenki territory: [skipped]

I thought it would be fair if other readers could take a look at those street views and judge whether or not they see any social non-uniformity.

Here is view from a point in between the two precincts in question. You can rotate the view with the mouse. The sign on the appartment building says "Underground parking spaces for sale: 1,800,000 rubles" ($57,000)

http://maps.yandex.ru/-/CFcOEB6w

And here is a view at another neighbor precinct which showed only 20% votes for Putin's party:

http://maps.yandex.ru/-/CFcOAB6h

 

reply to this comment

bbzippo

Quote:

Bingo! You've found them! This is a set of “ethnic outskirts” with the most crude  falsifications (and most evident ones, even without statistical figures). Some examples, selected:

 Enjoy Bashkortostan: http://ruelect.com/en/?tree_id=84

[skipped]

Any comments need there? 

And once again about KOIB. [skipped]

Thanks for checking out my presentation of the data. I have no doubts that crude falsifications took place in the ethnic regions. My point is that the fat tail is MUCH better correlated with geography than with KOIB penetration or than with the vote counting/reporting fraud as indicated at ruelect. Remove the 10 regions that I listed (C1 in my notation) - and the tail becomes no fatter than in any honest elections. So it is wrong to say that the tail is explained by fraud. In statistical terms, it is explained by location in the first place. 

We can then use whatever additional data we have to associate fraud with geography, but so far we do NOT have such data.

Enjoy Bashkortostan: http://ruelect.com/en/?tree_id=84

[skipped]

Any comments need there? 

I will have comments when I see data. So far, ruelect says that they have NOT received any voting protocols from those regions. The data that is there so far is only the official numbers. What was your point in refering to that data?

And once again about KOIB. [skipped]

I agree that the KOIBs might make it more difficult to rewrite the vote counts. KOIB penetration might be a useful variable that can detect and quantify fraud. What I was arguing is that they still allow to "stuff" (add) ballots. You keep refering to Shpilkin (podmoskovnik). His methods are based on the assumption that the vote-turnout correlation is explained only by stuffing. The ruelect data shows that very little stuffing took place: most of the discrepancies don't inflate turnout. So I'm only calling for diligent research. Since the appeals to the  "non-gaussianity" and the "unnatural correlation" have been shown unsound, let's scratch those theories and start looking at the more robust variables (ruelect, the koibs) in a more diligent manner.

What kind of huge contrast we can find to explain why United Russia’s support is 38% (turnout 59%) at the first precinct and 75% (turnout 71%) at the second one? Why 27-points gap between two neighbors?

 My neighbor and I have oposite political views. Surprised? My neighbor's house is 4 times more expensive than mine. Surprised?  A local legislative assembly candidate from the ruling party lives in an appartment building. He can use his connections and power to fix the roof and to fix other local issues. Surprised that the whole building votes for his party with a high turnout, while the adjacent building votes "normally"?

 

reply to this comment

Bobito

It is hard to take very seriously the statistical analysis made by a self-declared Republican voter.

reply to this comment

Alexei_Titkov

Quote:

If you are curious about the fat churosaur tail then it's easy to see to that it's mostly due to the ethnic outskirts. 

 

@bbzippo

Additionally, see one typical example of "ethnic diversity", "social contrasts" and so forth. 

Two neighbor precincts in the Moscow city, Ramenki territory:

Precinct # 2643: http://pics.livejournal.com/podmoskovnik/pic/00070qr9/

Precinct # 2644: http://pics.livejournal.com/podmoskovnik/pic/0006zx4g/

Precincts mapped (represented by red arrows):

http://pics.livejournal.com/podmoskovnik/pic/0007165w/

What kind of huge contrast we can find to explain why United Russia’s support is 38% (turnout 59%) at the first precinct and 75% (turnout 71%) at the second one? Why 27-points gap between two neighbors? I’m really confused, even after 20-year experience in studying  electoral geography of Russia.

reply to this comment

Alexei_Titkov

Quote:

Also, how the KOIBs could perevnt fraud by "merry-go-rounds" and "stuffing"? They are just ballot scanners. 

If you are curious about the fat churosaur tail then it's easy to see to that it's mostly due to the ethnic outskirts. See here http://bbzippo.wordpress.com/2012/01/04/russian-elections-dissecting-the-data/

  

Well, see where Churosaur’s tale grows.

Bbzippo says: “C1 (14% of counted votes): the top-left corner is apparently very well correlated with geography. Those are ethnic outskirts: Bashkortostan, Dagestan, Ingush, Kabardino-Balkar, Karachaevo-Cherkess, Mordovia, North Ossetia, Tatarstan, Tyva, Chechnya. (This identification is approximate).”

Bingo! You've found them! This is a set of “ethnic outskirts” with the most crude  falsifications (and most evident ones, even without statistical figures). Some examples, selected:

 Enjoy Bashkortostan: http://ruelect.com/en/?tree_id=84

Enjoy Dagestan: http://ruelect.com/en/?tree_id=147

Enjoy Ingushetia: http://ruelect.com/en/?tree_id=183

Enjoy Kabardino-Balkaria: http://ruelect.com/en/?tree_id=192

Enjoy Karachay-Cherkessia: http://ruelect.com/en/?tree_id=219

Enjoy North Ossetia: http://ruelect.com/en/?tree_id=356

Any comments need there? 

And once again about KOIB.

First, why they matters. Biggest falsifications were produced by re-writing results by precincts. In this case, fraudster can both add and subtract votes: add votes for their “right” party and subtract votes for other “wrong parties”. See kartaitogov

Scanners (KOIB) prevent subtraction, it’s only addition that possible in this case. That’s why falsifications fell down when KOIB used. That’s why Churosaur’s tale is much smaller when KOIB used: compare http://pics.livejournal.com/podmoskovnik/pic/0006bap0/ (KOIB works) and http://pics.livejournal.com/podmoskovnik/pic/0006d4k9/ (no scanners). Sample of terrotories (territorial commissions) is just the same in both cases. What a strange mystic "ethnic pecularites" that appear without scanners and disappear  when scanners start to work, just in the same locality. 

Churosaurs are quite delicate creatures, they eat and drink nothing but falsifications. They grow in Russia and don’t appear at the US elections.

reply to this comment

bbzippo

@Alexei_Titkov:

Russian "fraud studies" is not a pure game in statistics, they are based on empirical data of different sort. First of all, comparison between results approved by observers and results drawn without observers (see at: ruelect.com). Next, comparison between results counted automatically by scanner machines (KOIB) and results of hand-made calculation. Surprisingly, first ones are Gaussian and last ones - at the same territories - are Churosaur:

The results at ruelect.com is the ONLY "empirical data" about fraud that exists.

Surprisingly, first ones are Gaussian and last ones - at the same territories - are Churosaur:

Not true at all.

The observers' copies of the tallies at ruelect.com are NOT gaussian. Moreover, they disprove the assumption that the fraud introduced the correlation between turnout and party preference.

The distibutions at precincts with KOIBs are NOT gaussian either - they are just thinner tailed than the others.

"- at the same territories -" Not true. KOIB penetration strongly correlates with territory.

Also, how the KOIBs could perevnt fraud by "merry-go-rounds" and "stuffing"? They are just ballot scanners. So please make up your mind on the null hypothesis and the fraud model. If you trust the KOIB results then you have to admit that the vote-turnout correlation is natural. Which it is. If you say that fraud took place both during voting and during vote counting (which indeed was the case), then stop claiming that the fraud can be detected and measured statistically. It can't.

If you are curious about the fat churosaur tail then it's easy to see to that it's mostly due to the ethnic outskirts. See here http://bbzippo.wordpress.com/2012/01/04/russian-elections-dissecting-the-data/

 

reply to this comment

Mikhail Simkin

Quote:

Your theory for the peaks at 50%, 55%, etc is quickly refuted by noticing NO peak at 66% or 67%.

 

My theory is right because there are clear peaks at 1/3 and 2/3 in the American elections curves (see Figure 3)

http://www.alternativeright.com/main/blogs/district-of-corruption/the-bell-curve-doth-not-toll/

The peaks strongly depend on binning, however. We don't see such peaks in the Russian elections plot, but I did not make it myself, just took a ready figure from an article. I need to look at raw Russian election  data to make any conclusion.

 

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