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Summary

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Introduction

About two-thirds of the world’s democratic legislators are elected using PR.

Members of the U.S. House of Representatives are currently elected via single member districts (SMD). Most are elected using plurality rule, and a few using Ranked Choice Voting.

About two-thirds of the world’s democratic legislators are instead elected using PR. PR systems all feature multi-member districts (MMD): each legislative constituency elects more than one representative. The defining feature of PR is the approximate proportionality between a party’s vote share and its share of legislative seats.

Across and within PR systems, there is considerable variation in the number of seats per district, often referred to as district magnitude. For example, all 120 members of Israel’s Knesset are elected from a single national district, while the 155 members of Chile’s Chamber of Deputies hail from 28 districts with the number of members (“district magnitude”) ranging from three to eight.

PR systems usually impose a minimum threshold on a party’s vote share called the threshold of exclusion. If a party fails to achieve at least that share of the vote, it wins no seats. This measure is used to keep out very small or extreme parties. In Israel, for example, the threshold historically varied between 1% and 3.25%. Germany has a threshold of 5%.

Votes and Seats in a PR Election

The following section focuses on the most commonly-adopted variant of list proportional representation, or “list PR.” (2)

Consider a hypothetical election between two parties: Left and Right. The parties compete in a district with ten voters and two seats. Voters are presented with a ballot that lists the parties’ candidates in a specific order.

How voters fill their ballots depends on whether the list is open or closed.

Closed List

Under a closed list, votes are cast for a party list: voters cannot express a preference for any individual candidate. Suppose Left receives six votes and Right receives four votes. The party with the most votes wins the first seat—in our example, Left. The remaining seat is assigned on the basis of a specified rule. The most common is the “d’Hondt method,” first described by Thomas Jefferson in 1792. According to this rule, Left wins the second seat only if it has twice as many votes as Right. In our example, Left has six votes and Right has four, so Right wins the remaining seat.

Under the closed list system, the highest-ranked candidate on each party’s list takes the seat: Anna is elected from Left’s list, and Charlie is elected from Right’s list. Voters cannot determine the order in which candidates on the same list fill the seats.

Open List

Under an open list, voters can express votes in favor of specific candidates, in addition to party lists. Seats are again distributed between the parties based on their total list votes. However, seats are filled within each party based on how many votes each candidate received. In our earlier example, if Deborah wins four of the six votes going to the Right party and Charlie wins the remaining two, then Deborah takes the party’s single seat regardless of where she is placed on the party’s list. Under open list PR, voters therefore determine the order in which seats are filled with each party list.

Flexible List

Many real-world elections employ flexible list systems, which combine elements of open and closed lists. Votes can be for individual candidates, and if any candidate’s share of votes on the list exceeds a specified threshold, then she fills a party’s seat regardless of where she is ranked on the ballot. Lower-ranked candidates typically fail to reach these thresholds (3).

PR in the United States

A key insight from existing scholarship is that the consequences of replacing a single-member district system with PR ultimately depend on district magnitude and list openness. Together, these two features of institutional design determine the balance of power between parties (i.e., those who nominate candidates) and voters in how seats are filled.

However, the structure of the executive and the formal and informal party governance processes (e.g., the use of primary elections) are equally important for understanding these dynamics. While a large body of scholarship evaluates the consequences of switching from single member majoritarian systems to proportional representation, most of the evidence comes from parliamentary systems, not presidential systems like the United States.

The rest of this primer will evaluate some of the possible consequences of introducing PR in the United States, with a focus on 1. electoral campaigns or how elections are contested, 2. representation, i.e., who gets elected and what they do, and 3. accountability, i.e., how voters can use elections to discipline candidates and parties.

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Under any electoral system, candidates win office when they win the support of a sufficiently large coalition of voters.

The required size of this coalition depends on the electoral rule and the number of competing parties and candidates. In a two-candidate contest in a single-member district, that coalition is one half of all voters. More generally, with k candidates competing in a single-district race, a candidate can win with the support of just over 1/k share of the electorate. The smaller the required coalition, the stronger the incentive to appeal to an increasingly narrower constituency (4).

Less Targeting?

Under PR, the party that wins a majority of votes does not necessarily win every seat. In our earlier example with two seats, a party wins the second seat only if its vote share exceeds two thirds. Conversely, a party with a minority of support wins one of the two seats so long as its minority of support is at least one third of all votes cast. How does this impact parties’ strategies under PR? The answer depends on 1. parties’ goals and 2. how those goals are internalized by individual candidates.

In single-member districts, any additional vote in excess of a plurality has no impact on the outcome. Under list PR, however, a party can benefit from additional votes. In our example, a party that expands its majority from a one half to two-thirds is rewarded with an extra seat. Based on this intuition, early scholarship argued that PR encourages parties to pursue broadly appealing policy platforms in order to win as many votes as possible (5).

More recent work points out that this conclusion is contingent on electoral geography. It argues that PR may simply produce different patterns of targeted spending, rather than less overall targeting than plurality (6). Under plurality, a party targets local areas based on their relative responsiveness within each district. Under PR, by contrast, a party prioritizes local areas based on their relative electoral responsiveness without regard to district boundaries. When the sorting of voters with different electoral responsiveness to government spending (e.g., because of turnout or ideology) is sufficiently strong across districts, PR may even produce more geographically targeted spending than plurality.

The Role of List Openness

District-level electoral campaigns are contested by candidates. To what extent does PR help candidates internalize their parties’ national goals in their campaigning strategies? The answer depends on the balance of power between parties and voters in determining candidates’ electoral fortunes.

Under closed lists, party members decide the order in which candidates are ranked and, therefore, elected. The fifth-ranked candidate on a list in a district with eight seats wins office only if the party secures at least five seats. She therefore campaigns with the goal of expanding the party’s support as much as possible. Under open lists, voters decide the order in which candidates are elected. Regardless of her ballot rank, a candidate can be elected so long as the party wins at least one seat and her individual votes exceed her co-partisans’. This weakens her incentive to expand her party’s support relative to closed list PR (7). Instead, she will try to cultivate a “personal vote,”’ possibly at the expense of her party’s goals (8).

In sum: while not necessarily reducing incentives to targeted campaigns, list PR changes how parties value seats and the extent to which candidates try to expand their party’s electoral support.

The Role of District Magnitude

The most reliable empirical finding about PR is that it discourages two-party competition. Rather than aggregating the diverse interests of various groups of “policy demanders” to efficiently contest power (9), political parties can win seats despite representing the policy interests of a narrow segment of the electorate. Our two-seats example illustrates that a party can win a single seat with the support of only a third of the voters. With higher district magnitude, the required vote share is much lower.

Under open lists, candidates have weaker incentives to expand their party’s support relative to closed list PR.

In multiparty legislatures, small parties can play a pivotal role in legislative policymaking and extract significant benefits (10). And, size is not always an asset in legislative negotiations: smaller parties are actually more attractive coalition partners and are more likely to be included in legislative majorities than larger parties (11).

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PR changes the way in which voters hold parties and elected representatives accountable.

Collective Accountability

PR often produces multi-party legislatures. How does this impact legislative politics and executive politics?

Executive-legislative relations are shaped by the extent of electoral dependence between the two branches. In a parliamentary democracy, the executive’s survival depends on the support (or “confidence”) of a majority of legislators. Parliamentary systems generate a continuing mutual dependence between the executive and a majority coalition of legislators: the executive survives with that coalition’s support, and the government’s survival privileges its legislative coalition with policy rewards (12). PR tends to deliver multi-party executive coalitions in which the parties in government are collectively accountable to voters.

In a presidential democracy, instead, the chief executive and legislature are elected separately. When there are only two parties, either the president’s party has a majority, or the opposition party has a majority. The creation of multiparty legislatures in which no party has a majority reduces voters’ ability to assign responsibility for governance outcomes.

Because higher district magnitude tends to produce more fragmented legislatures, list PR also poses significant challenges for the aggregation of preferences relative to plurality systems. More parties entail a more diverse set of independently organized interests with their own control over candidate selection. As a result, support around bills may be negotiated on an ad-hoc basis with different parties, rather than consistently relying on the same legislative coalition (13). Unsurprisingly, the prevailing scholarly wisdom is that presidentialism and multiparty legislatures are structurally prone to gridlock, polarization and systemic instability (14).

The fragmentation of legislatures is associated with expanded legislative activism by presidents (15). In fact, some argue that in Latin America (the home of most presidential systems with list PR) the primary role of legislatures is to amend presidential proposals (16). In some countries, presidents institutionalize agreements with multi-party legislatures using cabinet appointments, thereby approximating the coalition agreements of a parliamentary democracy (17). This form of compromise is less likely to emerge when legislatures are highly fragmented, or when the president has powers of unilateral legislative prerogative (18).

Other presidential powers impact chief executives’ prospects for forming legislative coalitions. For example, line-item vetoes may paradoxically weaken presidents’ legislative effectiveness because they reduce their commitment to bundle policies into a single legislative package (19).

The Role of List Openness

Fragmentation also changes party leaders’ ability to enforce discipline within each party. The net effect depends on list openness. Under open lists, legislative leaders have weaker control over individual members’ reelection, and may struggle to enforce party discipline (20). Conversely, closed lists engender more discipline within each party’s legislative caucus, reducing the overall number of veto points in the negotiating process.

Depending on design choices, PR in the United States could therefore either expand the number of strong legislative leaders with veto powers, or further increase the veto power of individual legislators. This would likely change the role of legislative committees: because of the higher number of veto points, there is a stronger need for “stage management” at the committee level. Committees operate by strong consensual rules and are the main locus of bill negotiation, as observed in Latin America (21).

In sum: In a presidential system, PR results in more fragmented legislative coalitions and a more active presidential involvement in the legislative process. Its effect on legislative-executive relationships, however, depends on the structure of executive authority. Its effect on party discipline depends on list openness.

Individual Accountability

In PR systems, voters’ ability to select representatives and to discipline their behavior in office is again shaped by district magnitude and list openness. These factors affect the balance of power between “competing principals”: the potentially conflicting interests of constituency voters and party leaders (22).

The Role of List Openness

The subordination of legislators’ interests to party leaders depends in large part on list openness: closed lists encourage legislators to toe the party line— even at the expense of their constituents’ interests. The party’s control over a legislator’s list rank gives it outsized influence in her prospects of election. Promotion to a high list rank may all but guarantee her reelection; demotion to a low list rank may all but guarantee her defeat. By contrast, open lists encourage legislators to cultivate a “personal vote” through constituency service, ideological positiontaking, bill initiation and legislative dissent from their parties (23).

A benefit of open list PR is that it allows voters to decouple their choice of which party to support and which candidate to support (24). This contrasts with single-member plurality and closed list PR, in which the choice of candidates and party is effectively fused. The ability to separate these choices may help voters credibly punish poorly performing incumbents and therefore provide them with better incentives while holding office.

One might conclude that open lists always improve accountability. However, some individual vote-seeking activities may hamper the development of a party’s coherent ideological brand, and thereby weaken the party’s ability to pursue a common legislative agenda (25).

The Role of District Magnitude

Higher district magnitude (districts with more seats) interact with list openness in shaping the balance of power between voters and parties. Higher district magnitude gives parties even more power over legislators’ reelection prospects under closed lists; its impact on more flexible list variants is theoretically unresolved. It may also be difficult for voters to keep track of individual candidates in large district magnitude contexts, or to correctly assign responsibility amongst multiple co-partisan representatives.

This highlights a possible design trade-off: larger district magnitude may improve representation by reducing the wedge between a party’s seats and votes, but worsens accountability. Some scholars argue that small district magnitude in the region of two to five represent an electoral “sweet spot” that balances these competing goals (26). While there is evidence that list PR improves the ideological congruence between representatives and their voters, the impact on candidates’ quality and legislative effort is mixed (27).

In sum: List PR can improve representation of minority groups and voters’ policy preferences, but shifts control away from local voters and towards party leaders.

How Would Representation Change?

A party’s seat share in the legislature is an indirect measure of its influence on legislative policymaking. A party’s national vote share is a measure of its support amongst voters. Higher district magnitude under PR reduces the wedge between seats and votes, thereby making the legislature more representative of the electorate’s partisan preferences (28).

Recent examples highlight the severity of this wedge in single-member district systems. In the United Kingdom’s 2017 General Election, the Labour Party won 40% of the national popular vote and took 40% of seats in the House of Commons. In 2024, it won only 33% of the popular vote but took 63% of seats. The reason is that in single-member districts the distribution of a party’s votes across districts is critical. To win a seat requires a plurality of support in any given district: in 2024 Labour had a smaller vote share, but its support was spread very efficiently across districts.

In 2024, Labour therefore held barely one third of popular support and yet controlled almost twothirds of the legislature. This may benefit government stability—the UK is a parliamentary democracy— but it also has drawbacks. At a local level, minority interests may go unrepresented even in very evenly divided districts. An imbalance in local representation also translates to national imbalances in legislative representation; in 2024 Labour took a majority of 172 seats and can therefore implement a legislative program with almost no effective opposition from other parties, despite its relatively shallow popular vote. In the United States, these issues are also affected by gerrymandering.

Can PR mitigate these imbalances? The answer depends partly on design. If the design goal were exclusively to minimize seats-votes imbalances, one could choose a single national district such as Israel’s Knesset. In the United States, this would not only be unconstitutional but would also likely lead to undesirable levels of legislative fragmentation. Fortunately, evidence suggests that the benefits of larger district magnitude can be appropriated even with multiple districts and district magnitude in the single digits (29).

Electoral geography is another crucial factor for evaluating how PR shapes representation. Larger districts are more likely to favor a minority group that is geographically diffuse relative to one that is geographically concentrated.

To see why, consider an electorate consisting of thirty voters divided into two groups (A and B, reflecting religious, racial, or ethnic identities) and residing in one of three districts of equal size (1, 2, and 3). Suppose that 12 voters belong to group A and the remaining 18 belong to group B. Thus, group A is the minority and group B is the majority. Suppose the groups are evenly divided across districts: each contains four members of group A and six members of group B.

Under single-member districts, group B wins all three seats, so group A secures no representation. Under multi-member districts with two members in each district, each group wins one seat in each district. Finally, with three members in each district, Group A wins 40% of seats—matching its share of the population. PR helps group A to secure more representation.

Suppose instead that the minority group A is geographically concentrated in one of the districts. Suppose, in particular, that six members of group A vote in district 1, three vote in district 2, and three vote in district 3. In single-member districts, group A wins one third of seats. Under multi-member districts with two members per district, group A wins only a single seat (in district 1), and therefore its share of legislative representatives falls from one third to one sixth after adopting PR. Notice that if each district were to elect three representatives, group A again takes one third of the seats, and its total share of national representatives would be one third: no better than in single-member districts.

These stylized examples highlight the need to consider electoral geography when evaluating the effect of PR on minority representation. Correlation between district magnitude and political ideology may also impact representation (30).

In sum: List PR tends to improve the representation of minority groups that are evenly distributed geographically. It would also reduce the distortions associated with gerrymandering.

In line with the above idea, there is a consensus that list PR facilitates the election of women (31).

In 2024, the UK Labour party held barely one third of popular support and yet controlled almost two-thirds of the legislature.

Several lessons from our previous sections are also relevant: First, the strategies of parties respond to electoral incentives. The substantive content of party platforms may adjust as a consequence of switching to PR in ways that weaken the representation of minorities (32). Second, holding a seat as an independent party does not necessarily grant influence of the formation of legislative majorities (33). The expansion in the number of parties creates many opportunities for constructing legislative majorities. Whether minorities are best served by factions inside a small number of parties, or by independent parties in a more fractionalized legislature is in general ambiguous.

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Conclusion

Reforming a country’s election system from plurality to proportional representation has wide-ranging consequences: it impacts candidates’ electoral strategies, the number of parties that win legislative seats, their degree of internal discipline, and the relationship between the executive and legislature.

While many Western European countries have made that switch in the early 20th century, most of those transitions happened in the context of a parliamentary regime, not a presidential system. As a result, the associated empirical evidence is of limited relevance for the U.S. debate.

An important take-away is that many aspects of PR are partially design choices rather than intrinsic properties of the system. The extent to which voters control politicians’ incentives, rather than party leaders, largely depends on list openness. Trade-offs between legislative fragmentation and representation are shaped by district magnitude. The outcome of these design choices is mediated by other institutional features such as the legislative prerogatives of the president, as well parties’ internal norms and institutions.

Many aspects of PR are partially design choices rather than intrinsic properties of the system.

Electoral reform is a relatively rare event. Incumbents typically fare well under the status quo electoral rule, and are seldom motivated to change it. The strongest advocates are typically those that are disadvantaged under the inherited rule. Yet widespread dissatisfaction in the United States with many aspects of its political process—especially its deeply polarized two-party system—may give new impetus to electoral reforms that will likely lead to the formation of new electoral and legislative coalitions.

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References

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