Drawing a Line: Gerrymandering, Scale, and the Shape of a Vote
A state with 10 congressional districts must redraw after a census. The population is 55% Party A and 45% Party B, but Party A voters are concentrated in one dense metro area while Party B voters are spread evenly across the rest of the state. The legislature, controlled by Party A, draws a map in which Party A wins 8 of 10 seats. A reform group proposes an independent commission and a 'compactness' rule requiring districts to be as geometrically tight as possible. A second group proposes proportional representation instead of single-member districts.
1. Explain how Party A can win 8 of 10 seats with only 55% of the vote, using the concepts of packing and cracking. Note why the geographic concentration of Party A voters both helps and hurts them.
Read the worked answer
Packing: Party A's voters are already concentrated in the dense metro. Mapmakers can pack a huge share of Party A voters into a few metro districts so those districts are won by enormous margins - wasting thousands of 'surplus' votes that could have won other seats. Those packed seats are safe for A, but A 'wastes' votes there.
Cracking: Party B voters, spread evenly, can be cracked - split into many districts where they are a minority, so B loses narrowly across many seats instead of winning a few.
The paradox: Party A's concentration hurts them (it naturally packs them, wasting votes) but also helps them (as the mapmaker, they control where lines fall and can crack B). With 55% of the vote, a fair map might give A ~6 seats; deliberate packing + cracking yields 8. The concentration is a geographic fact; the 8-of-10 outcome is a choice about where to draw lines.
2. Evaluate the compactness rule as a remedy. Could a compact map still be unfair? Explain.
Read the worked answer
Compactness is not a fairness guarantee. A map can be perfectly compact and still biased, because bias comes from where voters are, not from district shape. If Party A is concentrated in a metro blob, drawing tight, compact districts around population centers can still pack A into a few seats and crack B across the rest - compactness and packing are compatible.
Compactness also conflicts with other legitimate goals: communities of interest (e.g., a rural region or a linguistic minority) may be spread across a non-compact area and need a district that follows its shape, not a tight polygon. A strict compactness rule could split such communities.
So compactness is a useful constraint against absurd shapes but a weak test of fairness. The real test is outcome-based: does the seat share track the vote share within a defensible range, and are minority/community interests preserved?
3. The second group proposes proportional representation. Identify the strongest geographic objection and how a designer might address it.
Read the worked answer
Strongest objection: single-member districts tie a representative to a place. PR with large multi-member or national lists can sever that link - voters in a rural county may have no identifiable local representative, and candidates may campaign to party lists in the capital rather than to any territory. This is a real loss of territorial representation.
Design fix: a mixed-member or regional-list system - keep local districts for territorial accountability but add compensatory seats so the overall seat share matches the vote share. Alternatively, use multi-member districts drawn around meaningful regions so lists still have a geographic anchor. The point to make: the trade-off is proportionality vs. local accountability, and good design can partly have both rather than treating them as mutually exclusive.