Graphing Russia’s Election Fraud

Following Russia’s parliamentary elections on December 4, a link was posted to Reddit reporting an impossibly high turnout (99.51%) and near unanimous support (99.48%) for Putin’s ruling party, United Russia, in the last location one would expect it: the republic of Chechnya. Even if relations with the secessionist region have improved since the Second Chechen War, both the turnout and United Russia’s vote share are a complete joke. This absurdity prompted a more thorough examination of all regions, many of which were also plagued by irregularities. In this post, I will give some detailed visualizations of both region- and precinct- level election data, and point out some highly likely instances of fraud.

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Visualizing 4+ Dimensions

As a student of pure math, I am often asked the question of how to visualize high dimensional objects. This question isn’t as important to pure mathematicians as it is to statisticians, so I write about it here.

…I’ve never had to visualize anything high-dimensional in my pure math classes. Working things out algebraically is much nicer, and using a lower-dimensional object as an example or source of intuition usually works out — at least at the undergrad level.

But that’s not a really satisfying answer, for two reasons. One is that it is possible to visualize high-dimensional objects, and people have developed many ways of doing so. Dimension Math has on its website a neat series of videos for visualizing high-dimensional geometric objects using stereographic projection. The other reason is that while pure mathematicians do not have a need for visualizing high-dimensions, statisticians do. Methods of visualizing high dimensional data can give useful insights when analyzing data….

More at http://www.lisazhang.ca/2011/12/visualizing-4-dimensions.html