Many posts have discussed reapportionment and redistricting -- much in the news now because of looming gerrymanders in Texas and California.
After months huddled around a whiteboard with a sharp graduate student, Richard Holden, fueled by too much bad Harvard Square coffee, we created a measure we call the “Relative Proximity Index.”
Picture every voter as a dot on the state map. First, we pin down the geometric minimum — the most compact way to bundle those dots inside the state’s jagged borders into its exact number of congressional districts, each with equal population, whether that means wrapping around Florida’s panhandle or hugging Georgia’s slanted shoulder. Then we compare the map the legislature actually draws to that floor. The ratio is the Relative Proximity Index. An R.P.I. of 1 means you’ve hit the geometric ideal; an R.P.I. of 3 means voters within a district would live — on average — three times as far apart than necessary.
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Since compactness isn’t the only legitimate redistricting criterion, we shouldn’t expect maps to hit 1.0. Lawmakers need room to respect county and city lines, comply with the Voting Rights Act and keep real neighborhoods intact. But compactness should be the starting point because it is neutral, measurable and easy to audit.
It subsumes contiguity (tight districts are, by construction, connected), discourages gratuitous splits of counties and cities, and helps protect genuine communities by forcing mapmakers to justify every detour. Start with the tightest lawful plan; if you deviate, say why, in public. As a rule: the bigger the R.P.I., the heavier the mapmaker’s thumb on the scale.
Our 50-state census of the 106th Congress — from 1999 through 2001 — turned up five of the least-compact maps: Tennessee (R.P.I. = 2.91), New Jersey (2.27), Texas (1.90), Massachusetts (1.87), and New York (1.83). To see what a strict maximal compactness rule would change, we looked at seat-vote curves — a standard political science tool showing how a party’s share of the statewide vote translates into seats — comparing current maps with compact redraws in California, New York, Pennsylvania and Texas.