Russian elections: heads and tails
In the previous post I separated the voting precincts into 3 categories and now I’m going to use 2 of them – C2 and C3 to take a look at the correlation between the vote ratio and turnout ratio. People say that such correlation must never be there in honest elections. If it’s there – they say – it means that ballot box stuffing took place. I already mentioned that I don’t see how party support and turnout can be uncorrelated. One argument that I mentioned was that both quantities are correlated with the precinct size. The other one is that one’s electoral activity cannot be separated from the political preferences. Now that I have virtually “removed” the correlations mentioned in the first argument, the only one remaining is the weak sociological one. Anyway, let’s get back to the data.
Vote ratio for United Russia vs. turnout ratio in C2 and C3:
Things to notice. First, both plots have fat vertical lines at 100% turnout (visible if you click the image). They are uncorrelated with the votes for UR and need a separate investigation. Second, C2 has a bad looking upper-right corner which may be yet another cluster consisting of smaller precincts. So let’s start with C3: it has a dense head and a tail. The head – they say – are the honest votes, and the tail is the stuffed ballots.
Ok, let’s assume that naturally all districts were sitting in the head (at 50% turnout and 30% party support). And then stuffing began. And what actually happens with the point on the diagram when we start stuffing ballots for UR in the box? Obviously – they say – it moves towards the upper-right. Not so simple. Let’s finally do a little math. We pick a precinct with let’s say 2000 registered voters. 1000 honest voters turned out and 300 of them cast ballots for UR. If we stuff x ballots then turnout becomes (1000+x)/2000 and the vote ratio (300+x)/(1000+x). As we increase x the point moves along a hyperbola (convex upward). When we stuff to the max (x=1000, 100% turnout), the vote ratio ends up being 65%.
Great improvement, but this shows that the linear tail that goes all the way to the upper-right corner cannot be obtained from a round-shaped “honest head” by the “stuffing transform”. Okay, maybe we are not seeing the true shape of the tail because the correlation between the turnout and precinct size still interferes (there is still some correlation left there). Let’s take a sample of precincts that have between 1950 and 2050 registered voters. There is no visible correlation between size and turnout in this case. But the tail still looks the same:
Am I saying that such tail cannot be a result of stuffing? No. Of course it can. The original honest distribution could have had some tail too. Even if you believe it must have been normal, you could still come up with a stuffing model that results in a straight tail. And here’s the vote-turnout plot of the general population:
Could the whole C2 category be a result of stuffing something that originally looked like C3? Sure, if we assumed that “honest” smaller precincts would show the same turnout and vote ratio as larger ones, and then they were all stuffed in some uniform manner. Unlikely? I don’t know.
All this “analysis” is only a game with numbers. Stuffing does not shape the data any differently than real party supporters who come and vote. Until we have a decent model of voter’s behavior, we can’t detect and measure any stuffing by looking at the data.
It is known from eyewitnesses that stuffing took place (at least, was attempted). Moreover, it is known from eyewitnesses (and photo/video evidence) that simple forging of tally sheets indeed took place. But without a model we cannot know how it shaped the data.
So, are there any models of voter behavior that we could apply here? We need to ask experts. I’m just having fun with numbers here. Here is, for example, a very simple “social conformity” model that was tested in (
or derived from? no, see the next post) prior Russian elections http://mpra.ub.uni-muenchen.de/14304/ . It indeed predicts correlation between the vote and turnout ratios. Also http://www.google.com/search?q=multinomial+model+elections could be helpful.