Justice Kagan opens her Callais dissent with a hypothetical. She knows it’s stylized, and she says so. Imagine a state shaped like a rectangle, with one of its six congressional districts a near-perfect circle in the middle. The circle is ninety percent Black. The other five districts, surrounding it, are ninety percent white. Voting is … Read more
A large strand of social network analysis treats triangles as special. Three people all connected to each other — a closed triad, a triangle in the graph-theoretic sense — show up in the literature as the minimum unit at which social structure is supposed to begin crystallizing. Triangles carry transitivity. They support trust. They coordinate … Read more
Last week’s post ended with a theorem. This one starts with a dashboard. The theorem — Arrow’s impossibility result, applied to the aggregation problem that Simpson’s paradox creates — is on the record in All Measurements Are Local if you want it. The short version: when subgroup results conflict with each other and with the … Read more