Riera (2013) showed that the effect of mixed-member electoral rules on district-level party fragmentation in the nominal (single-member district) tier is conditional on democratic experience: in a sample of 15 countries and 57 elections, unlinked mixed-member majoritarian (MMM) systems and close district races are associated with higher fragmentation only in young democracies. The paper left unexplained why this moderation occurs — whether it reflects endogenous electoral-system choice by strong parties in established democracies or genuine behavioural differences in candidate entry and voter coordination under young-democracy uncertainty — and how quickly voters and parties adapt once mixed rules are adopted or reformed. Later work has corroborated the broader claim that electoral experience conditions institutional effects (Raymond et al. 2016; Bunker and Negretto 2023), documented voter learning across electoral systems (Roussias 2022; Gómez Díaz 2022, 2024), and tested party-system legacies as a contamination mechanism (Vučićević 2025), but has not disentangled the mechanisms behind the MMM-by-democratic-age interaction at the district level in mixed systems, where even the sign of the MMM effect remains contested (Rich 2015). The problem is to provide a mechanism-resolving, dynamically informed, and specification-robust account of how democratic experience conditions electoral coordination in mixed-member systems, together with its implications for national party systems.

Background

Comparative research on electoral systems asks how institutional rules shape the number and size of parties competing for votes. A foundational proposition, Duverger's law, holds that electing one legislator per district by plurality vote (single-member districts, SMDs) favours two-party competition (see the classic statement in Riker 1982). Cox (1997) reframed this as a problem of electoral coordination: voters, candidates, and parties must converge on viable contenders or votes are wasted, and coordination failures produce fragmentation — more parties or candidates competing than the institutional incentive structure can sustain. Fragmentation is usually measured by the effective number of parties, N=1/∑ivi2N=1/\sum_i v_i^2, which weights each party by its squared vote share viv_i (Laakso and Taagepera 1979).

Mixed-member electoral systems elect a legislature through two simultaneous tiers: a nominal tier of SMDs and a list tier of seats filled from party lists. The two subtypes differ in whether the tiers are linked. In mixed-member proportional (MMP) systems (e.g., Germany, New Zealand), list seats compensate for nominal-tier outcomes so the overall result is broadly proportional. In mixed-member majoritarian (MMM, or parallel) systems (e.g., Japan since 1996, Russia until 2007, Lithuania), the tiers are unlinked and seats are simply added. A prominent literature argues that unlinked tiers 'contaminate' nominal-tier competition: parties unlikely to win SMDs still nominate candidates there to publicize the party and bolster its list vote, so SMDs under MMM carry more candidates and higher fragmentation than Duvergerian theory predicts (Herron and Nishikawa 2001; Ferrara, Herron and Nishikawa 2005).

Whether institutions translate into coordination also depends on political experience. In young democracies, voters and elites are uncertain about which parties and candidates are viable and party systems are weakly institutionalized, so coordination outcomes initially diverge from institutional expectations, converging only as electoral experience accumulates and the rate of electoral-rule change declines (Raymond, Huelshoff and Rosenblum 2016; Bunker and Negretto 2023). Separately, studies of institutional choice show that parties pick electoral rules to suit their own strength, so system type is itself endogenous to party-system features (Colomer 2005).

Pedro Riera's study 'Electoral coordination in mixed-member systems: Does the level of democratic experience matter?' (2013) brought these strands together. Using district-level data from 57 elections in 15 countries (more than 10,000 district observations), with Poisson and hierarchical linear models, he found that the level of democratic experience modifies the effect of other variables: the number of electoral parties is not uniformly lower in old democracies, and MMM systems and close district races are associated with higher nominal-tier fragmentation only in young democracies. The paper's conclusion lists several unresolved issues: the mechanism behind the MMM-in-young-democracies finding — stronger parties in established democracies enacting linked systems versus greater incentives for candidates to run despite low chances in unlinked tiers — has not been empirically disentangled; the interaction between district marginality and democratic age is significant only in the hierarchical linear models and not in the Poisson models, indicating sensitivity to model specification; the 15-country sample is underpowered for higher-level variables (ethnic fragmentation, presidentialism, decentralization); electoral volatility and electoral-system stability are unexplored alternative moderators, and how quickly voters adapt to new rules after a reform is unknown; the analysis is confined to district-level fragmentation, leaving national-level implications unexamined; and dynamic (panel or time-series cross-sectional) designs are needed to trace how coordination evolves and how quickly voter learning modifies institutional and competitiveness effects.

Problem Statement

Determine whether, and if so why, the effect of mixed-member electoral system type on electoral coordination in the nominal (single-member district) tier is conditional on the level of democratic experience, as reported by Riera (2013), including whether that conditionality survives alternative specifications, samples and measures — the sign of the MMM effect is itself contested (Rich 2015), and the conditionality may fail to survive robustness checks. The unresolved-issues discussion in the source's conclusion leaves four components unresolved. The conditionality survives only if the system-type-by-democratic-experience interaction retains its sign and statistical significance under every specification, measurement and sample considered in component 3; if it fails to do so in any one of them, the finding is one of non-survival, in which case the conditional effect that the mechanism, dynamics and implications components concern is not established. The four components are:

  1. Mechanism: identify, empirically, the mechanism behind the finding that unlinked mixed-member majoritarian (MMM) systems are associated with higher district-level party fragmentation in young democracies but not in established ones — disentangling at least the two candidate explanations raised there: (a) endogenous electoral-system choice, under which established democracies with stronger, more centralized parties adopt seat-linked (MMP) systems, so the moderation is a selection effect rather than a behavioural one; versus (b) behavioural coordination failure, under which weak parties in young democracies face greater incentives to nominate candidates in the unlinked nominal tier and voters coordinate more slowly amid uncertainty about candidate viability.

  2. Dynamics: establish the adaptation time path — whether, and if so how quickly, voters and parties in a young democracy approach the coordination levels characteristic of established democracies after a mixed-member system is introduced or substantially reformed, i.e., whether the MMM contamination premium (the excess nominal-tier fragmentation associated with unlinked tiers relative to the coordination Duvergerian theory predicts; see the contamination account in the Background) decays with democratic age, on what time scale, or whether it instead persists, and whether any decay reflects voter learning, elite candidate-entry adjustment, or both.

  3. Robustness and scope: establish whether the moderating interactions (system type by democratic experience, and district marginality or race closeness by democratic experience) are robust to model specification — including the discrepancy between count (Poisson) and hierarchical linear specifications reported in the source — to the measurement of fragmentation and of democratic experience, and to sample size and statistical power, given that the source's 15-country design is underpowered for higher-level variables (ethnic fragmentation, presidentialism, decentralization) and that alternative moderators such as electoral volatility and the stability of the electoral system itself remain untested. No measure of democratic experience and no young/established benchmark is fixed in advance here: specifying and justifying an operationalization, and testing sensitivity to it, is part of this dimension.

  4. Implications: characterize what these district-level conditional effects imply for national-level party system size and format.

No dataset is supplied with this task. For the empirical components, the solver is expected to obtain or assemble the required district-level data — an equivalent mixed-member-system sample of elections and districts, consistent with the source's 15-country, 57-election design or a larger one — and to state and justify the sample-inclusion criteria used.

References

  1. Riera, Pedro (2013). 'Electoral coordination in mixed-member systems: Does the level of democratic experience matter?' European Journal of Political Research 52(1):119-141. DOI 10.1111/j.1475-6765.2012.02064.x. https://doi.org/10.1111/j.1475-6765.2012.02064.x
  2. Laakso, Markku and Taagepera, Rein (1979). '"Effective" number of parties: a measure with application to West Europe.' Comparative Political Studies 12(1):3-27. DOI 10.1177/001041407901200101. https://doi.org/10.1177/001041407901200101
  3. Riker, William H. (1982). 'The two-party system and Duverger's law: an essay on the history of political science.' American Political Science Review 76(4):753-766. DOI 10.2307/1962968. https://doi.org/10.2307/1962968
  4. Cox, Gary W. (1997). Making Votes Count: Strategic Coordination in the World's Electoral Systems. Cambridge University Press. DOI 10.1017/cbo9781139174954. https://doi.org/10.1017/cbo9781139174954
  5. Herron, Erik S. and Nishikawa, Misa (2001). 'Contamination effects and the number of parties in mixed-superposition electoral systems.' Electoral Studies 20(1):63-86. DOI 10.1016/s0261-3794(00)00002-0. https://doi.org/10.1016/s0261-3794(00)00002-0
  6. Ferrara, Federico; Herron, Erik S.; Nishikawa, Misa (2005). 'The logic of contamination: district-level party systems.' In Mixed Electoral Systems: Contamination and Its Consequences. Palgrave Macmillan, pp. 33-48. DOI 10.1057/9781403978851_3. https://doi.org/10.1057/9781403978851_3
  7. Colomer, Josep M. (2005). 'It's parties that choose electoral systems (or, Duverger's laws upside down).' Political Studies 53(1):1-21. DOI 10.1111/j.1467-9248.2005.00514.x. https://doi.org/10.1111/j.1467-9248.2005.00514.x
  8. Rich, Timothy S. (2015). 'Duverger's law in mixed legislative systems: the impact of national electoral rules on district competition.' European Journal of Political Research 54(1):182-196. DOI 10.1111/1475-6765.12067. https://doi.org/10.1111/1475-6765.12067
  9. Raymond, Christopher D.; Huelshoff, Michael; Rosenblum, Marc R. (2016). 'Electoral systems, ethnic cleavages and experience with democracy.' International Political Science Review 37(4):550-566. DOI 10.1177/0192512115596368. https://doi.org/10.1177/0192512115596368
  10. Flick Witzig, Martina and Vatter, Adrian (2018). 'Electoral institutions, social diversity and fragmentation of party systems: a reassessment.' Swiss Political Science Review 24(1):1-15. DOI 10.1111/spsr.12285. https://doi.org/10.1111/spsr.12285
  11. Roussias, Nasos (2022). 'The evolution of new party systems: voter learning and electoral systems.' Political Studies Review 20(3):410-432. DOI 10.1177/14789299211014394. https://doi.org/10.1177/14789299211014394
  12. Gómez Díaz, Abelardo (2022). 'Still learning to make votes count? Electoral coordination in Mexico's mixed-member electoral system.' Election Law Journal: Rules, Politics, and Policy 21(3):229-248. DOI 10.1089/elj.2021.0074. https://doi.org/10.1089/elj.2021.0074
  13. Bunker, Kenneth and Negretto, Gabriel L. (2023). 'The party system effects of unstable electoral rules in Latin America.' Party Politics 30(6):1126-1142. DOI 10.1177/13540688231196111. https://doi.org/10.1177/13540688231196111
  14. Gómez Díaz, Abelardo (2024). 'Electoral coordination under simple and complex electoral systems: a time-series cross-sectional analysis.' Election Law Journal: Rules, Politics, and Policy 23(2):97-119. DOI 10.1089/elj.2023.0006. https://doi.org/10.1089/elj.2023.0006
  15. Golosov, Grigorii V. (2024). 'Electoral rules and the two-party system: a methodological inquiry with reference to Duverger's law.' International Political Science Review 46(3):388-405. DOI 10.1177/01925121241283715. https://doi.org/10.1177/01925121241283715
  16. Vučićević, Dušan (2025). 'The legacy of the past: pre-reform party competition and contamination of single-member districts in mixed electoral systems.' Public Choice 204(1-2):181-201. DOI 10.1007/s11127-025-01289-y. https://doi.org/10.1007/s11127-025-01289-y
  17. Bunker, Kenneth (2025). 'Challenging conventional wisdom in new democracies: social diversity, electoral rules, and party system fragmentation in Chile.' Election Law Journal: Rules, Politics, and Policy 25(1):56-79. DOI 10.1089/elj.2024.0064. https://doi.org/10.1089/elj.2024.0064
  18. Bunker, Kenneth (2026). 'Electoral reform and party-system fragmentation: diminishing marginal effects and vote-seat conversion limits in Chile's concurrent local elections.' Local Government Studies (online first), pp. 1-26. DOI 10.1080/03003930.2026.2704044. https://doi.org/10.1080/03003930.2026.2704044