Statistics presented below can nicely demonstrate manipulations in the last elections in Moscow
Here is the figure that shows how a percentage got by a political party in a voting district (y-axis) depends on voter's turnout as a percentage of total number of voters. The funny thing is that for all parties except for the ruling "Edinaja Rossia" (United Russia) backed by Medvedev and Putin, there is no correlation between the voter's turnout and the results of elections, while for "United Russia" (blue dots) there is a nice upward trend.
Source of the figure is here
Question: how does this pattern can be explained>
H0: by pure chance. Probability of this really is almost surely zero
H1: voters of United Russia are very heterogeneous -- they are very active in some areas of Moscow and very passive in other areas. This heterogeneity is not observed for supporters of other parities
H3: An invisible hand messed around with the results of elections
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