The Coalition That Lost the Popular Vote but Won the Chamber
A country elects its 200-seat legislature from 100 single-member districts, each choosing one member by plurality. A reform party wins 42% of the national vote but only 18 seats, because its supporters are spread thinly across districts. A regional party wins 9% of the vote but 30 seats, because its supporters are concentrated in a few districts. The two largest parties, with 49% combined, hold 152 seats and form a governing coalition. Public approval of the legislature falls to 28%. A civic group proposes replacing the system with proportional representation (PR) using multi-member districts and a national threshold of 5%.
1. Explain how single-member plurality districts translate votes into seats in a way that produces the reform party's 18 seats and the regional party's 30 seats, and identify the two distinct distortions involved.
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In single-member plurality, a seat is won by the largest share in a district, not by a national share. Two distortions follow:
- Wasted votes / underrepresentation of diffuse support. The reform party's 42% is spread thinly, so it finishes second or third in most districts and wins few seats (18). Its votes are "wasted" because they do not translate into district pluralities. This is a seat-vote distortion.
- Concentration bonus / overrepresentation of geographically clustered support. The regional party's 9% is concentrated, so it wins pluralities in many of its districts and captures 30 seats - more than triple its vote share. This is a geographic efficiency effect.
The two distortions point in opposite directions: the same rule punishes diffuse minorities and rewards concentrated ones. The 49% coalition holding 152 of 200 seats (76%) illustrates the manufactured-majority effect.
2. Evaluate the PR proposal against the stated problems. What would PR fix, what new problems might it create, and what should the civic group weigh before endorsing it?
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What PR fixes: seats track national vote share more closely, so the reform party's 42% yields roughly 84 seats and the regional party's 9% yields roughly 18 - removing both distortions. Fewer wasted votes; more accurate representation of diffuse opinion.
New problems: (1) Fragmentation - many small parties; coalition formation becomes harder and governments less stable. The 5% threshold is a deliberate brake, but it also excludes parties below it, recreating a (smaller) wasted-vote problem. (2) Weaker constituency link - multi-member districts and party lists can reduce the tie between a member and a specific district. (3) Accountability - voters may find it harder to identify whom to hold responsible.
What to weigh: the group's actual goal - if it is proportionality, PR addresses it; if it is local accountability, PR trades some away. The threshold level, district magnitude, and list type (open vs. closed) determine how much fragmentation and accountability loss occur. A defensible recommendation states the tradeoff explicitly rather than treating PR as strictly superior; the 28% approval figure reflects distrust of the outcome, which PR may or may not cure.