The Conversion Problem
An electoral system converts votes into seats. It determines how public preferences become power.
Three components do most of the work:
| Component | What it fixes | Effect |
|---|---|---|
| District magnitude | Seats per constituency | The strongest determinant of proportionality |
| Electoral formula | How votes become seats | Majoritarian, proportional, or mixed |
| Threshold | Minimum support to qualify | Excludes small parties |
District magnitude is the decisive one. A single-seat district cannot divide its seat. Therefore, it cannot be proportional under any formula. Proportionality rises as magnitude increases.
The Three Families
- Majoritarian. The winner takes the seat. These systems routinely award a party with 40% of the vote an absolute majority of seats.
- Proportional. Multi-member districts allocate seats by vote share using divisor methods like D'Hondt or Sainte-Laguë. D'Hondt favours larger parties, while Sainte-Laguë is more neutral.
- Mixed. Voters elect members from both districts and lists. In mixed-member proportional systems, list seats compensate to ensure proportional totals. In parallel systems, they do not.
Spain uses closed lists with D'Hondt and a 3% district threshold. However, small rural districts keep its overall result far less proportional than expected.
Effects on Party Systems
Duverger's law states that single-member plurality favours two-party systems, whereas proportional representation favours multiparty systems.
This outcome occurs through two distinct mechanisms:
- Mechanical: the seat allocation rules directly deny seats to smaller parties.
- Psychological: voters abandon uncompetitive parties to avoid wasting votes.
Plurality systems often maintain more than two parties nationally when minor parties concentrate their support regionally.
Measuring Electoral Results
- The effective number of parties weights parties by their seat or vote share. For example, a 40/40/10/10 split yields an effective count of roughly 2.6.
- The Gallagher index measures the disproportionality between vote shares and seat shares. Scores in the low single digits represent proportional outcomes.
Common pitfall: treating proportional representation as a single, uniform system. Variations in magnitude, thresholds, and formulas mean two proportional systems can function entirely differently.