  We introduce a non-partisan probability distribution on congressional
redistricting of North Carolina which emphasizes the equal partition of the
population and the compactness of districts. When random districts are drawn
and the results of the 2012 election were re-tabulated under the drawn
districtings, we find that an average of 7.6 democratic representatives are
elected. 95% of the randomly sampled redistrictings produced between 6 and 9
Democrats. Both of these facts are in stark contrast with the 4 Democrats
elected in the 2012 elections with the same vote counts. This brings into
serious question the idea that such elections represent the "will of the
people." It underlines the ability of redistricting to undermine the democratic
process, while on the face allowing democracy to proceed.
