Concept and basic effects
Rae (1967) first showed that the gap between vote and seat shares shrinks as district magnitude grows. Taagepera and Shugart (1989) saw magnitude as more decisive than the allocation formula, and Lijphart (1990) confirmed this with comparative data. Plurality with magnitude one tends toward two parties, as in Duverger's law, while proportional representation with large districts is linked to multiparty systems.
The M+1 rule and party numbers
Cox (1999) summarized the M+1 rule: with magnitude M, strategic coordination by voters and elites tends to limit viable candidates or parties to about M+1. Measured by Laakso and Taagepera's (1979) effective number of parties, larger magnitudes bring more parties, but Benoit (2001) found that the effect depends on formula and social diversity.
The sweet spot debate
Carey and Hix (2011) argued that low-magnitude PR districts of roughly four to eight seats greatly improve representativeness without excessively multiplying parties, creating a 'sweet spot' that combines representation and accountability. The argument is often cited in debates over mixed-member systems and multi-member district reform.
FAQ
- What is district magnitude in simple terms?
- How many legislators a district elects. One member means magnitude one; five members means magnitude five.
- What changes when magnitude is larger?
- Small parties win seats more easily, results track vote shares more closely and the number of parties tends to grow.
Sources reviewed: 2026-10-26
References
- Rae, D. W. (1967). The political consequences of electoral laws. Yale University Press. The first quantitative treatment.
- Taagepera, R., & Shugart, M. S. (1989). Seats and votes: The effects and determinants of electoral systems. Yale University Press. Magnitude as the decisive factor.
- Lijphart, A. (1990). The political consequences of electoral laws, 1945–85. American Political Science Review, 84(2), 481–496. Magnitude and proportionality.
- Cox, G. W. (1999). Electoral rules and electoral coordination. Annual Review of Political Science, 2, 145–161. The M+1 rule.
- Benoit, K. (2001). District magnitude, electoral formula, and the number of parties. European Journal of Political Research, 39(2), 203–224. Magnitude versus formula.
- Carey, J. M., & Hix, S. (2011). The electoral sweet spot: Low-magnitude proportional electoral systems. American Journal of Political Science, 55(2), 383–397. The electoral sweet spot.
- Laakso, M., & Taagepera, R. (1979). "Effective" number of parties: A measure with application to West Europe. Comparative Political Studies, 12(1), 3–27. The effective number of parties.