Diverse Representation: Proportional Representation

Marcus Ogren
10 min readMar 27, 2022

This is the third post in a four-part series on the effects of voting methods on female and minority representation:

  1. Districts vs. Block Plurality
  2. Comparing Single-Winner Voting Methods
  3. Proportional Representation
  4. Conclusions

Proportional representation (PR) means that any sufficiently large minority can cast their ballots in a way that ensures they are represented. This minority can be political/ideological (e.g. a smaller political party), geographical, racial, ethnic, religious, age-based, or anything that voters care about.

Whether a minority is large enough is determined primarily by district magnitude, which is the number of representatives elected from each district. We can talk about district magnitude without actually having districts — we just treat the entire jurisdiction (be it a city or an entire country) as a single district. A district magnitude of 1 means having single-winner elections — and a voting bloc needs to comprise over 50% of voters to ensure representation. With a district magnitude of 2, a voting bloc typically only needs the support of over 1/3 of voters to get represented, and with a district magnitude of 5 (as would be common if the Fair Representation Act is passed) a mere 1/6 of voters are needed. With a Party List voting method, it is natural to elect all the representatives in a single election without districts, so the district magnitude can be well over 100 and even small minorities can ensure that they are represented.

However, using a proportional voting method does not mean that all sufficiently large minorities will be represented in proportion to their share of the electorate; a minority must value its representation enough to vote in a way that will see people from that minority elected. For example, high school dropouts do not typically have a preference to elect other high school dropouts, so high school dropouts end up being underrepresented in a way that is entirely compatible with their preferences. More significantly, PR does not ensure that women will comprise half of an elected body since relatively few voters care about electing women substantially more than they care about electing candidates of any gender who agree with them on the issues. Female voters could act collectively to ensure that at least half of elected officials are women, but they don’t.

Proportional Representation and Minorities

Sufficiently large racial and ethnic minorities get represented under PR. Racial and ethnic minorities tend to vote cohesively enough to elect minority candidates under PR. This is significantly easier than under Block Plurality, which is winner-take-all and fails to systematically provide any minority representation, and single-winner districts, which only enable minority representation when those minorities are clustered together. Proportional representation yields strong minority representation regardless of their geographical distribution. Empirically, the semi-proportional methods of Cumulative Voting and Limited Voting result in greater Black representation than either districts or Block Plurality. (We call these methods semi-proportional because they result in many wasted votes and are reliant upon excellent strategic coordination among voters to achieve proportional representation. They still outperform Plurality, however.)

This is the most basic mechanism for PR improving minority representation: minority voters voting for minority candidates, and electing them (despite being a minority) because it takes a smaller fraction of the vote to get elected under PR than in winner-take-all elections. But it’s not the only mechanism. Even in cases where a minority isn’t large enough to guarantee itself a seat, a relatively small group of liberal White voters who want to improve minority representation can join forces with that minority to elect someone.

Imagine a city with a poor side of town and a rich side of town. The poor side is 30% Black, 70% White, and the Whites there prefer to elect White people. The rich side of town is almost entirely White, but many of the Whites there are liberals who want to have a Black city council member. With an at-large Block Plurality election, the Whites who want to elect White people outnumber the Blacks and the Whites who want to elect Black people put together, so White candidates will probably win every seat. If the city uses single-winner districts, Whites will still win all the seats; the districts on the poor side of town will still elect Whites if you can’t draw a majority-Black district there, and the districts on the rich side of town won’t have Black candidates since so few Black people live there. But with proportional representation, Black voters and White liberals can work together to elect Black candidates from the poor side of town. This works even if the total Black population is substantially less than the amount required to win a seat, as determined by district magnitude.

Proportional Representation and Women

We can expect PR to help women for the same reasons that we can expect multi-winner elections to help women in general:

  • When political parties and other groups that endorse candidates are in a position to support multiple candidates for the same race, there is often pressure on them to support a comparable number of women and men.
  • Voters who tend to prefer men to women in single-winner elections may still want to strive for a somewhat gender-balanced elected body by also supporting some women in multi-winner elections.
  • There is less of an incentive for negative campaigning in multi-winner races, so insofar as women prefer not to run when there’s an expectation of mudslinging they may be more willing to run for office in these races.

(The first two points can also apply to racial/ethnic minorities; just as political parties and voters can be reluctant to support only men they can also be reluctant to support only Whites.)

To assess the effects of PR on women’s representation empirically we can look at either international comparisons or at countries that use PR in only some of their elections. The international comparisons clearly show that PR is correlated with greater female representation. One notable study found that the use of PR had a larger impact on female representation than female workforce participation or the percent of female college graduates. However, we don’t have anything close to a randomized controlled trial, so we can’t infer causation with any confidence. If the same cultural factors that lead to countries using PR also lead to more women running for office (for example), we could see such a correlation even if PR did nothing to cause the improved representation of women. For this reason, I believe that comparing female representation in elected bodies that were elected in the same country using different voting methods is the more reliable approach.

The clearest comparison comes from Australia, where the Senate is elected multi-winner districts using Single Transferable Vote (Proportional RCV) and the House is elected in single-winner districts using Instant Runoff Voting (single-winner RCV). You can read a study about it, but the data are clear enough that all it takes is one look at this chart:

In every year since 1943 (the first year a woman was elected to the Parliament of Australia), a larger fraction of Senators have been women than House members. This cannot be a coincidence, and it also can’t be attributed to cultural factors since the same voters are electing the House as are electing the Senate. There is no reasonable explanation aside from the different voting methods.

An interesting counterpoint comes from Japan, which used a semi-proportional voting method called Single Nontransferable Vote (SNTV) prior to 1994. (SNTV is very simple: there is a multi-winner election, but each voter can only vote for one candidate.) In addition, Japan used single-winner Plurality (which is what SNTV becomes with a district magnitude of one) and Party List to elect some members of its national legislature. By far the greatest fraction of women were elected under Party List — but there was no difference between SNTV and single-winner Plurality.

Under SNTV, the usual explanations for why multi-winner elections help women didn’t hold. Japan had weak parties, where candidates were competing more on their own brands than on the brand of their party, so efforts by political parties to nominate more women would have been ineffective. And for voters, there was no option of supporting both women and men — SNTV only lets you support one candidate. The Japanese experience shows that there’s more to improving women’s representation than simply using some multi-winner voting method; which multi-winner method you use also matters.

Comparing Proportional Voting Methods

The primary mechanism by which PR helps racial and ethnic minorities — empowering large enough minorities to elect one or more candidates of their choice even if the majority of the electorate opposes them — should be equally effective under all proportional voting methods. It may be somewhat less effective under semi-proportional voting methods that require minorities to vote strategically in order to be fully represented, but we should expect the main differences between PR methods to lie in electing women and in electing minorities via secondary mechanisms.

My best guess is that Party List — especially the closed list version, where parties have total control over which of their candidates get elected — is the best for electing women. Political parties will often adopt voluntary (or in many countries, involuntary) quotas for nominating women, and this is easier and more effective with Party List elections than when voters choose which of a party’s nominees get elected. It is worth noting that most any proportional voting method can behave like Party List if the parties are strong enough; this appears to be largely the case in Australia’s senate, where “above the line” voting (in which voters choose to rank parties instead of candidates and use each party’s ordering of its candidates) is common.

I suspect that Mixed-Member Proportional systems (MMP) are worse for women than other proportional voting methods since MMP involves a great many single-winner elections. However, the international comparisons don’t seem to back me up on this; New Zealand has gender parity under MMP, and Germany is not particularly bad. (I found claims that German women fared better for the list seats than for the constituency seats, but I couldn’t find any numbers.) International comparisons involve a lot of extraneous factors, and my best guess is that cultural differences are why New Zealand has gender parity rather than some counterintuitive virtue of MMP. But it’s evidence that the disadvantage of MMP compared to other PR methods (if it exists) isn’t that big.

How about candidate-based proportional voting methods like STV, Sequential Proportional Approval Voting (SPAV), and Allocated Score (Proportional STAR Voting)? A relevant difference between these methods and Party List is that Party List works with an arbitrarily large district magnitude, but the candidate-based methods become unwieldy with a district magnitude greater than about half a dozen since it’s unreasonable to expect voters to research a large number of candidates and the ballots become enormous. (Australia uses STV with a district magnitude of 12 for some of its Senate elections, but it’s definitely unwieldy.) In terms of parties and voters wanting to support both men and women, electing five or six candidates in a race isn’t much worse than supporting dozens of candidates since they’ll tend to think about gender equality either way. But it’s actually party magnitude (how many seats a party will win in a given race) that matters, not district magnitude. A district magnitude of 5 will often mean a party magnitude of just 1 or 2, and if a party or political faction will only win one or two seats, having all of their winners be male does not seem particularly outrageous.

How do the candidate-based proportional voting methods compare to one another? We only have data on STV; while Sweden used SPAV in the early 20th century I don’t know of any research on it, and no governmental election has been conducted using Allocated Score. Therefore, we’ll have to settle for speculation.

Presumably, two of the biggest factors influencing women’s success and the success of minorities reliant on winning votes from Whites are the degree to which a voting method encourages voters to provide support for multiple candidates (as is evidenced by the failure of SNTV to help women) and the degree to which it makes such support valuable. These factors cut in opposing directions:

  • STV incentivizes voters to rank as many candidates as possible — there’s literally no downside to it — but the lower rankings are far less valuable than the top one.
  • Under SPAV, all support is equally valuable, but there are big downsides to voting for many candidates. Doing so may cause a merely tolerable candidate you voted for to defeat your favorite candidate since your ballot doesn’t express a preference between the two, and voting for a candidate who would win anyway greatly diminishes your power to elect additional candidates (without sending that power to other likeminded voters as happens with STV and Allocated Score). Under SPAV it’s often strategically optimal to only vote for a single candidate, and SPAV is no better than SNTV at encouraging people who vote this way to vote for a woman.
  • Allocated Score is an in-between option; support from voters who don’t give you the highest rating is more valuable than under STV, and there’s less of a downside to scoring multiple candidates highly under Allocated Score than to voting for multiple candidates under SPAV. Giving several different candidates a score of 3 or higher is strategically sound since doing so won’t reduce your influence in future rounds, unless you end up in their quota in which case you at least increase the influence of like-minded voters. Also, a score of 3 is 3/5 as valuable as a score of 5.

My best guess is that Allocated Score is the best of these three methods for female and minority representation and SPAV is the worst, and I find it plausible that SPAV is closer to semi-proportional methods like SNTV than to STV in this regard. But this is still speculation without empirical evidence; for instance, it’s plausible that most voters will vote for approximately as many candidates under SPAV as there are winners and that SPAV will do the best of all these voting methods. We know that tried and true proportional voting methods like Party List and STV are far better for women and minorities than single-winner districts, and, in the absence of empirical evidence or theoretical grounds to think otherwise, most likely SPAV and Allocated Score will be substantially better as well.

Next post in this series: Conclusions



Marcus Ogren

I am an advocate of better voting methods which eliminate the spoiler effect, make third parties viable, and yield proportional representation.