Some simple numeric examples to make a point that I've been trying to make for a while (although without the extensive amount of examples reported by the author of this article).

There's no way of grouping voters into districts that doesn't introduce distortions.

Sure, some politicians may be tempted to play the card harder than others. Some may purposefully redraw maps in ways that dilute the votes for their opponents. But eventually *any* groupings introduce distortions that can be played by either side.

We often hear that the best solution to districting issues is to have smaller district. But the math easily proves that the distortions are removed only when the size of each district tends to one - i.e. when we get rid of districts entirely.

You just can't be fine-grained locally while being fair globally at the same time.

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