Proportional representation

Pragmatic reform and mathematical complication

Most political scientists interested in electoral reform are big fans of something called proportional representation. What is proportional representation? What can proportional representation do to improve the democratic processes that create your government? What are some examples of proportional representation in action? What are the limitations of proportional representation?

The phrase “proportional representation” refers both to a goal and also to some of the electoral systems that are designed to better achieve that goal. The goal of proportional representation isn’t to elect the legislators who are individually the best legislators; it is to elect a group of legislators that do a good job of reflecting the diverse opinions and interests of the electorate.

Single-member districts

Among those studying single winner voting systems, the gold standard for a bad voting system is the plurality vote. Among advocates for proportional representation, the gold standard for a poorly representative system is the use of single member districts where each separate member of the legislature is elected completely independently.

Each seat then corresponds to a distinct group of voters (constituency). As suggested by the widespread use of the name “single member district,” these constituencies are usually assigned as a physical geographic unit (district), although in some cases constituencies are assigned to ethnic groups, tribes, or other identifiable sub-units of the population.

Typically, using separate single-member constituencies means that the party with the largest plurality is overrepresented. Regional parties with strong pockets of geographic strength can also be overrepresented. For example, in the United Kingdom general election of 2019, the ruling Conservative party won 56% of the seats with a plurality of 42% of the popular vote, and the regionally-concentrated Scottish National Party won 7.4% of the seats with 3.9% of the popular vote. By contrast, the Liberal Democrats won a geographically diffuse 7.4% of the vote, earning only 1.8% of the seats.

It is also possible for the party to win a plurality of seats without winning a plurality of the vote. On the national level, this happened in the United Kingdom in 1951 and 1974, and more recently in the United States in 2012. In the United States, examples at the state level happen routinely. In most cases, this is due to gerrymandering.

Gerrymandering is the practice of drawing district boundaries in such a way as to increase the disproportionality of the results. It is not unusual for proportional voting methods to use single-member districts for elections, but the results are adjusted in one way or another to ensure that results are proportional. This makes gerrymandering irrelevant or nearly irrelevant, so it tends not to happen in systems with proportional representation.

Multi-winner does not mean proportionate

Electoral systems designated as types of proportional representation are multi-winner systems; however, not all multi-winner systems are proportionate. Most voting rules produce a natural ranking of options. Single-winner electoral systems disregard all but the first place ranking; and a multi-winner electoral system may simply use the same voting rule.

Using a candidate ranking from an approval vote will tend to reflect the views of a broad consensus of voters, but is not likely to lead to representation of minority perspectives. Historically the general ticket or unit rule, where all candidates are placed on one ballot together and voters are allowed to vote for at least as many candidates as seats, has not led to good representation of minority parties.

This type of rule has been most notably used in the United States. It was frequently used in House of Representatives elections prior to 1842, when the Apportionment Act of 1842 mandated the use of single member districts. While general tickets is no longer used for House of Representatives elections in any state, the unit rule is presently used by 48 states for selecting electors for the Electoral College.

How to achieve proportionality

The key to achieving proportional representation is to group candidates together in such a way that limits the number of similar candidates elected. There are two common methods that are described as “proportional representation.”

The first method is to count votes for parties and then assign a number of seats to each party based on the number of votes. Seats are then assigned to candidates within those parties in order to achieve an electoral outcome where the proportion of seats matches the proportion of parties. This is commonly used in continental Europe, and is probably the most common form of proportional representation worldwide.

The advantage of this version of proportional representation is that it can use a simple plurality ballot while sidestepping most of the problems with plurality voting. If nearly all voters’ first-place preferences translate into parliamentary representation, the fact that plurality voting does not account for secondary preferences is almost irrelevant.

The second method is to use a single-winner voting rule iteratively, and eliminate the ballots of voters who are “satisfied” once they have achieved representation. The most notable example of this technique is in the Australian Senate, but it is also used for Irish parliamentary elections. In both of these cases, the exact rule is an iterative version of a plurality count. In the past, satisfied ballots were eliminated by random draw; in the era of computer-assisted counting, an averaged version of the satisfied ballots can be subtracted.

The advantage of this version of proportionality is that it can account for significant differences between individual candidates within the same party. In some cases, politicians within the same political party may vary significantly. The drawback is that it is more complex, both for voters and for the officials responsible for tallying ballots.

The example of the Slovenian National Assembly

The national legislature of Slovenia has ninety seats. Two are filled using separate single-winner elections that use a Borda count; these two seats have ethnic constituencies (Hungarians and Italians). The country is also divided into eighty-eight districts that are grouped into eight constituencies of eleven districts.

For the eighty-eight seats determined by proportional representation, the parties run candidates in each district. Votes for the candidate in that district are counted as votes for the party.

Parties with less than 4% of the total national vote are eliminated from consideration entirely, regardless of how well they may have done in one isolated district. In 2022, since Slovenia’s party system was fairly fragmented, 24% of the vote went to minor parties that received less than 4% of the vote. This was fairly a significant share of the vote, and five of the parties that dropped under the threshold had won a combined total of thirty-seven seats in the previous election.

Next, quotas are assigned to each party both on the national level and on the constituency level. The quota system used slightly favors larger parties. For example, the new Freedom Party earned 34% of the total vote, which translated to 41 seats (46% of the total) at a rate of 10,000 votes per seat; the Social Democrats earned 7% of the total vote, which translated to 7 seats (8% of the total) at a rate of 11,000 votes per seat.

Finally, each party’s seats are assigned to their most individually successful candidates within each of the eighty-eight districts. This is called an “open list” system. If the party chose the order of candidates, it would be a “closed list” system. At the end of the process, every district has a representative who ran as a candidate in that district, and all parties have their assigned quota of members of Parliament.

The example of the New Zealand House of Representatives

New England has a 120-member legislature that is elected with a mixed member proportional system. Each voter casts two plurality ballots: One for their local legislator, and one for a national party. This means that a voter may choose to vote against the local candidate that represents the party they prefer nationally, or vote in favor of a local candidate whose party they dislike nationally.

72 members are elected directly (these are known as electorate seats), and then the 48 tother seats in the House are assigned by party list at large in a way that makes up for any disproportion (these are known as list seats). Parties are not awarded list seats unless they either earn 5% nationally or win at least one electorate seat locally.

For example, in the 2020 election, 11% of New Zealanders voted for a party that fell below the national threshold. The New Zealand Labour Party’s candidates won 46 districts (63% of all districts), but only 50% of the total party vote, and so received 19 list seats for a total of 65 seats. The Green Party won only 1 district, but 8% of the vote nationally, and so received 9 list seats for a total of 10 seats.

If a party wins more electoral seats than its national party vote allocation allows, then extra list seats are assigned to make up for these “overhang” seats. In 2011, for example, the Māori Party won 3 electorate seats with only 1.4% of the party vote, so an extra list seat was allocated for a 121-member House.

The limits of voting for parties

One issue that arises in considering the practice of voting for political parties directly is that political parties are comprised of individual politicians. The actual course charted by a party following elections may be determined by political negotiation after elections; individual politicians may also break with the party on key issues. History is full of examples of striking differences between politicians who shared the same party label.

For example, the United States of 1960, the Democratic Party included both Strom Thurmond and Hubert Humphrey, while the Republican Party included both Barry Goldwater and Nelson Rockefeller. The division among Republicans was stark enough that both “Goldwater Republican” and “Rockefeller Republican” were in widespread use after Goldwater’s nomination in 1964. When Hubert Humphrey spoke out against segregation at the 1948 Democratic convention, southern delegates stormed out and nominated Strom Thurmond to run for president instead of Harry Truman.

In general, the major advantage ascribed to closed-list systems is that they can improve party coherency and discipline; overall, any system involving voting for lists rather than candidates relies heavily on party coherency and discipline to function correctly. Proportional systems that elect individual candidates directly, such as the single transferrable vote system, avoid this problem; but electoral systems that elect individual candidates rely on voters being familiar with those candidates.

Fragmentation and viability

Similarly, list-based systems can struggle when the party system is changing rapidly enough that voters have trouble identifying which parties will meet the viability threshold. This is one of the reasons why almost one quarter of the votes in the 2022 Slovenian election discussed above were wasted on parties that did not get any seats at all; the party system was in a state of flux.

Even when the party system itself is fairly stable, as in the example of the New Zealand 2020 election discussed above, a significant number of ballots (in that case about 10%) may be wasted on minor parties that fall below a viability threshold. Ballots wasted on non-viable candidates are a feature of plurality voting in general, rather than list-based proportional representation systems in particular; but it’s a problem with plurality that remains significant in proportional representation systems with typical party viability thresholds on the order of 4–5%.

One of the main motivating examples behind the widespread use of viability thresholds within proportional representation systems is the Weimar Republic; there is a common idea that Hitler’s rise to power was the result of unfettered proportional representation and the large number of very small minor parties with non-zero parliamentary representation. (I am skeptical of this claim. I especially recommend against the notion that an Electoral College type system would have prevented Hitler’s rise to power.)

Concluding remarks

Another major limitation of proportional representation in general is that the principle of proportionality cannot be meaningfully applied to unique offices that are elected by themselves. Some countries stand to benefit more clearly from proportional representation than others. For the United Kingdom, proportional representation could change the whole face of the government just by changing the way the House of Commons is elected. Proportional representation may be the best prospect available for electoral reform in the United Kingdom.

For the United States, the governing structure includes a singular president, singular state governors, and two separately-elected federal senators assigned to each state. At the current assigned size of the House of Representatives, the federal representatives from the seven smallest states are also elected one at a time. Short of sweeping constitutional changes, full-scale proportional representation could only be implemented in state legislatures, and a limited level could be implemented in the House of Representatives at the level of state delegations.

There is a very strong argument that state legislatures in the United States should be elected by proportional representation. Individual state legislators are fairly obscure politicians that voters do not know very well. The state-level versions of the national parties are more often coherent without regional subdivisions. Finally, the election of the state legislature is administered by a single state under a uniform set of rules and practices set by the state. This means that gerrymandering problems tend to be worse, but also means that, in contrast to the federal House of Representatives, proportional representation can be targeted at the level of the whole assembly.