Electoral systems

Intuition [Beginner]

An electoral system is the set of rules that determines how votes are translated into seats in a legislature. The same voters, with the same preferences, can produce very different results depending on which rules are used.

Imagine an election where 40% of voters support Party A, 35% support Party B, and 25% support Party C. Under one set of rules, Party A might win every seat. Under another, the three parties might split seats in proportion to their vote shares. Neither result is "wrong" -- they follow from different choices about what an election should achieve.

The basic choices are:

• Winner-take-all: the candidate with the most votes in a district wins the single seat. Also called plurality or first-past-the-post.
• Proportional representation: parties receive seats in proportion to their share of the vote. Many seats are allocated from each district or nationwide.
• Mixed systems: some combination of the two, with some seats filled by winner-take-all and others by proportional allocation.
• Ranked-choice systems: voters rank candidates in order of preference rather than choosing just one. Lower-ranked candidates are eliminated and votes are redistributed until someone has a majority.

No electoral system is neutral. Each one rewards certain strategies, favors certain kinds of parties, and disadvantages others. The choice of system is itself a political decision.

Visual [Beginner]

Major electoral systems compared

System	How votes become seats	Key countries	Typical outcome
First-past-the-post (FPTP)	One seat per district; most votes wins	US, UK, Canada, India	Two large parties; single-party governments
Proportional representation (PR)	Seats allocated by national or regional vote share	Netherlands, Israel, South Africa, Brazil	Multiple parties; coalition governments
Mixed-member proportional (MMP)	Some seats by FPTP, rest by PR to make overall result proportional	Germany, New Zealand	Multiple parties; coalition governments
Parallel (mixed-member majoritarian)	Some seats by FPTP, some by PR, but PR seats do not compensate	Japan, South Korea, Russia	Large party advantage; some smaller parties
Single transferable vote (STV)	Multi-seat districts; voters rank candidates; surplus votes transfer	Ireland, Malta, Australian Senate	Proportional outcomes with candidate choice
Instant-runoff voting (IRV/RCV)	Single-seat districts; voters rank candidates; lowest eliminated until majority	Australia (House), Maine, Alaska	Majority winner without separate runoff
Two-round system	If no majority in first round, top two face runoff	France, many African and Latin American countries	Majority winner; expensive second round

How the same votes produce different results

Assume a country with 5 districts, each with 100 voters:

District	Party A	Party B	Party C	FPTP winner	PR seat allocation (5 seats total)
1	42	35	23	Party A	--
2	40	38	22	Party A	--
3	38	37	25	Party A	--
4	35	40	25	Party B	--
5	45	30	25	Party A	--
Totals	200	180	120	A: 4 seats, B: 1 seat	A: 2, B: 2, C: 1

Under FPTP, Party A wins 4 of 5 seats with 40% of the vote. Under PR, the three parties split seats proportionally: A gets 2, B gets 2, C gets 1. Neither system is wrong -- they measure different things.

Worked example [Beginner]

Consider how Germany's mixed-member proportional system works in practice.

Each voter gets two ballots:

1. First vote (constituency ballot): Choose a candidate for your single-member district. Winner takes the seat, just like FPTP.
2. Second vote (party ballot): Choose a party. This determines the overall proportion of seats each party receives in the Bundestag.

The total number of seats a party receives is determined by the second vote. If a party earns 25% of the party vote, it gets roughly 25% of the total seats. The constituency winners from the first vote are counted first. Any remaining seats are filled from party lists to bring the total up to the proportional share.

This means constituency wins are guaranteed (each district has a direct representative), but the overall composition of parliament reflects the national party vote. A party that wins few constituencies but gets 10% of the party vote still enters parliament with roughly 10% of the seats.

Germany also has a 5% threshold: a party must win at least 5% of the national party vote (or 3 constituency seats) to enter parliament. This prevents fragmentation while still allowing smaller parties representation.

Compare this with the United Kingdom, which uses pure FPTP. In 2015, the UK Independence Party (UKIP) received 12.6% of the national vote but won only 1 of 650 seats. Under Germany's MMP system, UKIP would have received roughly 80 seats. The difference is entirely a product of the electoral rules.

Check your understanding [Beginner]

Formal definition [Intermediate+]

An electoral system is the set of rules governing how votes are cast, counted, and translated into seats. The key variables are:

1. Ballot structure: whether voters choose candidates (candidate-centered) or parties (party-centered), and whether they express a single preference or rank multiple options.

2. District magnitude: the number of seats allocated per electoral district. This is the single most important variable. Single-member districts (magnitude 1) produce majoritarian outcomes; larger districts enable proportionality.

3. Electoral formula: the mathematical rule for converting votes into seats.

Formula	Description	District magnitude needed	Disproportionality
Plurality	Most votes wins	Single-member	High
Majority (runoff/IRV)	Winner needs >50%	Single-member	Moderate to high
D'Hondt (PR)	Divisors: 1, 2, 3, 4... allocate seats sequentially	Multi-member	Low to moderate (favors larger parties)
Sainte-Lague (PR)	Divisors: 1, 3, 5, 7...	Multi-member	Low (more neutral)
Largest remainder (PR)	Seats = votes / quota; remainders awarded to highest remainders	Multi-member	Low

4. Thresholds: minimum vote share required to receive seats. Common thresholds: 5% (Germany, Poland, Turkey), 4% (Sweden), 3% (Greece), none (Netherlands, South Africa). Higher thresholds reduce fragmentation; lower thresholds increase representativeness.

5. Assembly size: the total number of seats. Larger assemblies can be more proportional because each seat represents a smaller share of the total.

Duverger's law (Duverger, 1954): Single-member plurality systems tend to produce two-party competition. The logic is psychological: voters avoid "wasting" their vote on a third party unlikely to win, and strategic politicians avoid joining or creating third parties. This is a tendency, not an iron law. India and Canada use FPTP but have multiparty systems, because regional parties can win pluralities in specific districts even without national support.

Key concepts [Intermediate+]

Proportionality indices. Political scientists measure how closely an electoral system translates votes into seats using disproportionality indices. The most common is the Gallagher Index (Least Squares Index), which calculates the square root of half the sum of squared differences between vote shares and seat shares.

Country (recent election)	Gallagher Index	System
Netherlands	~1.0	PR (no threshold)
Germany	~2.0	MMP
Ireland	~3.0	STV
France	~10.0	Two-round
UK	~12.0	FPTP
US	~15.0+	FPTP (plus Electoral College for president)

Lower values indicate more proportional results. Values below 2 are considered highly proportional; values above 10 indicate significant disproportionality.

Mechanical vs. psychological effects. Electoral systems shape party systems through two channels (Duverger, 1954):

• Mechanical effects: the direct translation of votes into seats. Under FPTP, a party with 10% of the vote receives roughly 0% of the seats. Under PR, it receives roughly 10%.
• Psychological effects: voters and politicians adapt their behavior to the system. Voters desert parties they perceive as non-viable. Politicians join larger parties or form pre-election alliances. Over time, these strategic adaptations reinforce the mechanical effects.

Gerrymandering: the practice of drawing electoral district boundaries to favor a particular party or group. FPTP systems are vulnerable to gerrymandering because the distribution of votes across districts determines who wins. PR systems are largely immune because seats are allocated proportionally regardless of district boundaries.

Feature	FPTP systems	PR systems
Gerrymandering possible?	Yes, critically important	No (or minimal impact)
Who draws boundaries?	Legislature, commission, or court (varies)	Less relevant
Examples of reform	US: independent commissions in some states; UK: Boundary Commissions	Less applicable

Exercises

Exercise 1. New Zealand switched from FPTP to MMP in 1996. Before the switch, parliament was typically dominated by one or two parties. After the switch, six or more parties regularly entered parliament. Explain this outcome using Duverger's framework.

Reveal

Under FPTP, Duverger's psychological effect was strong: voters deserted smaller parties (Social Credit, Values Party, Alliance) because they could not win pluralities in single-member districts, even though these parties had significant national support. The mechanical effect then confirmed this: even when smaller parties won 10-20% of the vote, they won few or no seats. After switching to MMP, the mechanical effect changed: a party winning 5% of the party vote was guaranteed proportional seats. The psychological effect followed: voters felt free to support smaller parties, and new parties formed. The result was a transition from a two-party-dominant system to a multiparty system with regular coalition governments.

Exercise 2. Some countries use compulsory voting (Australia, Belgium, Brazil). How might compulsory voting interact with the choice of electoral system?

Reveal

Compulsory voting reduces the impact of turnout differentials between groups. Under voluntary voting with FPTP, parties can win by mobilizing their base rather than persuading the center, because many voters simply stay home. Compulsory voting forces parties to compete for the entire electorate, which can moderate political discourse. Under PR, compulsory voting ensures that the full spectrum of public opinion is represented in the seat allocation, rather than just the preferences of the most motivated voters. However, compulsory voting can also increase the number of informal (spoiled) ballots from disengaged voters and raises questions about whether forcing participation is compatible with democratic freedom.

Political theory [Master]

The fairness question: what should an electoral system achieve?

Electoral system design rests on competing values that cannot all be maximized simultaneously:

• Proportionality: seats should reflect vote shares. Favors PR.
• Governability: the system should produce stable, effective governments. Favors FPTP or high thresholds.
• Accountability: voters should be able to identify and sanction responsible leaders. Favors systems with clear constituency links.
• Representation of diversity: the legislature should reflect the demographic and ideological diversity of the electorate. Favors PR with low thresholds.
• Simplicity: voters should understand how their vote translates into representation. Favors FPTP.
• Local representation: voters should have a identifiable representative for their area. Favors single-member districts.

Lijphart (1999) argued that proportionality and governability are not actually in tension: PR systems with coalition governments produce policy that is more representative and, empirically, no less stable than FPTP single-party governments. His comparative data showed that consensus democracies (PR systems) outperformed majoritarian democracies (FPTP systems) on measures of democratic quality, economic performance, and social welfare, though this finding is contested.

Gerrymandering and the problem of neutral districting. In FPTP systems, the drawing of district boundaries is itself a political act. The question of how to draw districts "fairly" has generated extensive theoretical and mathematical work:

• Partisan fairness: the seat-vote curve should be symmetric -- both parties should receive the same share of seats for the same share of votes.
• Competitiveness: districts should be drawn to create competitive races rather than safe seats.
• Community of interest: districts should group voters with shared interests or identities.
• Compactness: districts should be geographically compact (the "ugly district" test).
• Racial fairness: in the US, the Voting Rights Act requires districts that give minority voters a chance to elect candidates of their choice.

These criteria can conflict. A competitively drawn map may split communities of interest. A racially fair map may produce irregular shapes. Mathematicians (Duchin, 2018) have developed ensemble methods that generate thousands of possible maps to determine whether a proposed map is an outlier relative to what neutral map-drawing would produce.

The paradox of electoral reform. The actors who control electoral system design (incumbent legislators) are precisely the actors who benefit from the existing system. Taagepera and Shugart (1989) observed that electoral reform is rare because it requires the winners of the current game to change the rules in ways that would reduce their advantage. When reform does occur, it is usually driven by external pressure (public demand, judicial rulings, crisis) rather than voluntary action by incumbents. Japan (1994), New Zealand (1996), and Italy (multiple reforms) all reformed their electoral systems after political crises.

Electoral systems and polarization. The relationship between electoral systems and political polarization is debated. Some scholars argue that FPTP contributes to polarization because candidates in safe districts appeal to their party base rather than the median voter. Others argue that PR contributes to polarization because extremist parties can enter parliament and pull the discourse toward extremes. The empirical evidence is mixed, suggesting that electoral systems interact with other factors (party rules, media environment, social cleavages) to produce polarization.

Historical context [Master]

Pre-modern elections. Elections are ancient -- the Catholic Church elected popes, Venice elected its Doge, the Holy Roman Empire elected its emperor -- but these were not popular elections in the modern sense. They involved small elites choosing among candidates, often through complex indirect procedures.

The expansion of the franchise and the emergence of modern electoral systems. As suffrage expanded in the 19th century (from propertied elites to all adult men, then to women), the question of how to translate votes into representation became urgent. The British system of single-member districts developed organically over centuries. Proportional representation was developed as a conscious reform proposal in the mid-19th century, most influentially by Thomas Hare (1859) and John Stuart Mill, who argued that FPTP left large minorities unrepresented.

The 20th century: PR spreads, then retreats. Many European countries adopted PR in the early 20th century as suffrage expanded and working-class parties demanded representation. Germany's Weimar Republic (1919) used pure PR with no threshold, producing a fragmented parliament that contributed to political instability -- a history that informed the 5% threshold in post-war Germany's MMP system. Some countries that adopted PR later reverted: Italy experimented with PR, then moved toward a mixed system; France shifted between PR and two-round systems several times.

Post-war institutional design. Germany's MMP system (1949) was specifically designed to combine the local accountability of FPTP with the proportionality of PR, while avoiding the fragmentation of Weimar. Japan adopted its single non-transferable vote system (SNTV) under American occupation, which produced factional competition within the dominant LDP rather than inter-party competition. After the Cold War, many newly democratic states in Eastern Europe adopted PR systems, influenced by West European models.

Recent reforms. New Zealand's switch from FPTP to MMP (1996), approved by referendum, is the most studied case of democratic electoral reform. Japan shifted from SNTV to a mixed system in 1994. The UK held a referendum on adopting IRV in 2011, which was defeated. Several US states and municipalities have adopted ranked-choice voting since 2000 (Maine, Alaska, New York City, San Francisco). The trend in established democracies has been toward systems that increase proportionality or voter choice, though reform remains politically difficult.

Bibliography [Master]

• Duverger, Maurice. 1954. Political Parties: Their Organization and Activity in the Modern State. Wiley.
• Gallagher, Michael, and Paul Mitchell, eds. 2005. The Politics of Electoral Systems. Oxford University Press.
• Lijphart, Arend. 1999. Patterns of Democracy. Yale University Press.
• Norris, Pippa. 2004. Electoral Engineering: Voting Rules and Political Behavior. Cambridge University Press.
• Rae, Douglas. 1967. The Political Consequences of Electoral Laws. Yale University Press.
• Renwick, Alan. 2010. The Politics of Electoral Reform. Cambridge University Press.
• Taagepera, Rein, and Matthew Shugart. 1989. Seats and Votes: The Effects and Determinants of Electoral Systems. Yale University Press.
• Duchin, Moon. 2018. "Gerrymandering Metrics." In Political Geometry, ed. Duchin and Ruiz.
• Farrell, David. 2011. Electoral Systems: A Comparative Introduction. 2nd ed. Palgrave Macmillan.
• Katz, Richard. 1997. Democracy and Elections. Oxford University Press.