We study in this paper the influence that redistricting can have on the result of elections.
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First, we propose a definition of diversity of the distribution of legal electoral maps of a state, to capture the gerrymandering potential; then, for a specific electoral map of a state, we propose a definition of outliers (positive outlier or negative outlier with respect to a given political party), to identify the states where the electoral map ought to be audited. We apply this approach to the French system, that has legal constraints very different from the U.S., much more granular and much less balanced. We first show that despite the legal constraints, there is some large diversity of maps, and as a consequence it is possible to draw the maps in order to favor one specific party in the aggregate (over all states). Then, we show that many states are positive or negative outliers, with a large imbalance between different parties. This calls for a specific audit of redistricting in those states, to examine whether the current map is indeed drawn in a way to advantage or disadvantage some party. This is the first computer study of gerrymandering potential in France.
