Diverse Representation: Comparing Single-Winner Voting Methods

Marcus Ogren
12 min readMar 19, 2022

This is the second 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

Research on Instant Runoff Voting

In American cities that have adopted Instant Runoff Voting (single-winner Ranked Choice Voting), women and minorities have greater success than in cities that use Plurality, and their representation also tends to improve in a city after that city adopts IRV. But these observations tell us virtually nothing about how effective IRV is at causing more diverse representation. The cities that have adopted IRV have tended to be exceptionally liberal and diversity-valuing, so it’s no surprise that female and minority representation is greater in those places. And it’s not only places where IRV has been adopted that have seen more diverse representation — the phenomenon exists nationwide. In short, such trends tell us next to nothing about the efficacy of IRV; it takes a more sophisticated approach to determine causation.

Sarah John, Haley Smith, and Elizabeth Zack have taken such an approach in their 2018 study of the California Bay Area. They use a differences-in-differences methodology to isolate causation by studying four California cities that have adopted IRV and nine control cities with similar demographics. They look at:

  • Female/minority representation in the cities that now use IRV, prior to them adopting IRV
  • Female/minority representation in those cities after adopting IRV
  • Female/minority representation in control cities prior to 2010 (the year that all of the four IRV cities other than San Francisco adopted IRV)
  • Female/minority representation in control cities after 2010

They perform a regression analysis with three variables related to the introduction of IRV (in addition to a bunch of variables to control for differences in demographics and the like): Treatment (1 if a city is an IRV city, 0 otherwise), Time (a binary variable saying whether IRV has been adopted yet for an IRV city or whether it’s 2010 or later for a control city), and Time*Treatment, the product of the other two variables. When better female/minority representation is positively correlated with Treatment, it could mean that a city’s representation is improved by adopting IRV — or that the cities which adopted IRV were uncommonly inclined to elect women/minorities to begin with. But when better representation is positively correlated with Time*Treatment, the previous hypothesis can’t explain it.

John, Smith, and Zach find statistically significant improvements in the fraction racial/ethnic minority candidates, the fraction of female winners, and the fraction of female minority winners. (They also find statistically insignificant improvements in the fraction of female candidates, the fraction of female minority candidates, and the fraction of (not necessarily female) minority winners.) However, the finding that women started winning more often in the IRV cities than the control cities was driven by a decrease in female representation in the control cities, and was only significant at the p<0.1 level:

A graph showing fewer women elected in control cities post-IRV.
Here, AV = the alternative vote, another name for IRV

(It’s a similar story with female minority winners: roughly the same fraction won in control cities pre-2010 as in IRV cities pre- and post-IRV, but far fewer won in control cities post-2010.)

One possibility is that there was a regional trend of less female representation — but that adopting IRV protected cities from this trend. In this case, IRV would deserve full credit, and we could expect it to yield better representation for women in the future as well. The authors note,

Generally, across the U.S. the number of women serving in elective office declined or stagnated between 2008 and 2014. For example, the number of state legislators peaked after the 2008 election (at 24.3%) and did not reach those levels again until 2014.

This is basically true, but the effect size is tiny. According to the Center for Women in Politics, the percentage of women in state legislatures peaked at 24.7% in 2010 (I’m guessing the data have been updated since this study was published), fell to a low of 23.8% in 2012, and only surpassed 2010 levels in 2017. By contrast, female representation (as predicted by John, Smith, and Zach’s model) decreased by eleven percentage points — from 40% to 29% — in control cities. The nationwide change doesn’t come close to explaining this. Ultimately, I find it far more likely that the finding on how often women win was driven more by coincidences in the control cities than by anything related to IRV.

So what should we conclude, based on the empirical research? It would be a mistake to say that the evidence shows IRV is better for women — but it would be a greater mistake to say that the evidence shows IRV isn’t better for women. The truth is, we need more data. John, Smith, and Zach’s study was well-designed but underpowered; it couldn’t detect something like a hypothetical 5% increase in female representation as a result of IRV. I am hopeful that similar studies with larger datasets will give us some clear answers in the next ten years, but for now, we have to accept that there’s a lot of uncertainty. And it should be emphasized that their finding that IRV leads to more minority candidates running for office does hold up to scrutiny; it was driven by increases in the IRV cities, as one would expect of a real effect, and was statistically significant at the p<0.05 level.

Why might IRV be better for women and minorities than Plurality?

John, Smith, and Zach offer three reasons why they expect IRV to elect more minority candidates:

Firstly, because voters can rank multiple candidates without fearing that they will hurt the chances of their most preferred candidate, we might expect some white voters — even some who would not usually vote for a minority candidate in a single-winner election — to rank minority candidates second (or third) (Darcy et al., 1985; King, 2002).

Secondly, minority candidates may be able to work or campaign with candidates from other communities to gain second, and third, choice support from voters in other minority communities with whom they share similar experiences, interests and political preferences. It has long been accepted that African-American voters vote overwhelmingly for black candidates (See: Philpot and Walton, 2007). At the local level in non-partisan elections, where there is often little information about candidates and no party labels to guide voters, Barreto (2007) and Abosch et al. (2007) show that Hispanic voters are politically cohesive, supporting Hispanic candidates over other candidates. When there is no candidate from the group’s ethnicity in the race, endorsements from community leaders and other coethnic individuals can encourage voters to vote for someone from a different identity group, especially African-American leaders encouraging African-American voters (Benjamin, 2017). If a minority candidate were to encourage their supporters to voters to rank a candidate from another minority group second, and the candidate from the other minority reciprocates, those candidates would maximize their respective chances of winning.

Thirdly, we expect fewer consequences of vote splitting between candidates from the same minority group. In the case studies studied here, the mean number of candidates running for each seat before the introduction of [IRV] was 3.3 (3.7 in the cities that adopted [IRV]). This, in part, reflects the fact that these local elections are non-partisan, in which political parties cannot formally limit candidate entry. Additionally, filing fees and signature requirements for many local offices are low. The high average number of candidates per seat indicates that vote splitting and the spoiler effect are likely to be at play in these elections under plurality or majority runoff. Some white candidates surely experience defeats in plurality and majority runoff that can be accounted for by vote splitting between two or more like candidates. However, the effect of vote splitting is likely greatest for candidates with strong support in communities that exhibit the most racially cohesive voting patterns, like African-American and Latino communities. For candidates from these groups, the loss of part of their community’s vote to another candidate from the same community poses a greater risk to their candidacy. [IRV] should significantly mitigate that risk.

Most of these reasons are incomplete because they don’t mention an asymmetry between Whites and minorities. Yes, White voters can rank minority candidates second — but why exactly should this be more common than ranking White candidates second? (Since the publication of this study, FairVote has found that minority candidates pick up more support during the tabulation of IRV, though FairVote is far less careful than John, Smith, and Zach and this finding could easily be due to something extraneous such as having more candidates in districts with greater minority populations.) And yes, if minority candidates endorse candidates from different minorities by saying, “rank her second” that will help all of these minorities, but why should this be more common than White candidates cooperating in a similar way?

Furthermore, the claim that “the effect of vote splitting is likely greatest for candidates with strong support in communities that exhibit the most racially cohesive voting patterns” doesn’t add up. Imagine you have some set of candidates, and then cloning all of the candidates such that voters are indifferent between a candidate and that candidate’s clone. Under Plurality, this will halve each candidate’s vote total (due to half of the votes going to clones), but it can never change who wins (aside would-be winner’s clone winning instead of them). This fact is unaffected by dividing the electorate into factions that may or may not be cohesive.

These factors may be part of an explanation for how IRV could help minorities, but I’d need something more fleshed out to be persuaded.

A far more promising explanation for why IRV yields more minority candidates is that it reduces the fear of vote-splitting:

[P]olitical parties, like community groups, exert pressure on would-be candidates to de facto limit candidate entry, and community groups can endorse particular candidates and campaign against others if it is necessary to prevent vote splitting. Under [IRV], there are fewer reasons to engage in these behaviors.

Here, finding an asymmetry between minorities and Whites is easy. If a faction wants to field one candidate and there’s a White guy and a Black woman thinking of running, and some influential people within that faction are a little bit racist or sexist, which of these wouldn’t-be candidates is more likely to be told to wait their turn and refrain from entering the race?

When it comes to differences in electing women, John, Smith, and Zach focus on the role of negative campaigning, noting that “women were deterred from running for office by aspects of modern campaigning, most notably negative campaigning.” They also hypothesize that women’s campaign styles are more effective under IRV than under Plurality:

Women profess a dislike of the negativity of modern campaigning (Lawless and Fox, 2012), and may be less likely to engage in negative campaigning than men when they are competing in an environment that does not reward it. Phrased alternatively, women may be more inclined to conciliatory campaigning than men in environs that reward conciliatory campaigning. In this way, female candidates campaigning in [IRV] elections might be better at garnering voters’ second choices, as their conciliatory style may avoid alienating other candidates’ supporters

While I haven’t investigated claims of how women campaign differently than men (the authors describe such ideas as “largely untested theories about women’s campaigning style”), the claim that IRV reduces negative campaigning has empirical support and is intuitively obvious. Under Plurality, if you aren’t a voter’s first choice there’s no downside to alienating that voter by launching dishonest attacks against their favorite. Under IRV, such tactics could lead to this voter ranking every candidate above you.

Another possible benefit to women and minorities is that perceptions of electability matter less under IRV than under Plurality. Women are actually as likely to get elected as men, but most voters don’t know that, and as a result, they are liable to vote for a man they like slightly less over the woman who is their sincere first choice in a Plurality election. IRV mitigates this dilemma since ranking a candidate who can’t win first typically results in one’s vote getting transferred rather than wasted.

Finally, analogously to Block Plurality, voters might feel sexist about having all of their three highest-ranked candidates be men even if they wouldn’t feel sexist about voting for a man under single-winner Plurality, and this could result in additional support for women. Similarly, voters may also want to show some support for minority candidates by not having all of their top rankings be filled by white people.

Comparing single-winner voting methods

None of the theories for why IRV may be better for women or minorities is exclusive to IRV, though you may have to replace phrases like “rank second” with ones like “score highly”. While we don’t know which of these theories are correct or important, we can still make some informed speculation as to which single-winner voting methods should do better than others if a particular theory is correct.

If reducing the fear of vote-splitting is important, any reasonable voting method should substantially outperform Plurality. Perhaps Approval Voting would slightly underperform other voting methods due to excessive bullet voting by non-strategic voters, but such differences should be relatively minor.

If reducing campaign negativity is important, we can’t say much more without refining our hypothesis. Plurality is the only (single-winner) voting method that probits voters from supporting multiple candidates in some fashion, so it should carry the smallest penalties for negative campaigning and therefore yield the most negative campaigning. But this tells us nothing about how other voting methods compare.

We can identify two forms of positive/collaborative campaigning: “Vote for her too”, where candidates encourage their supporters to also support a rival to some extent (such as with a #2 ranking), and “Vote for me too”, where candidates try to convince another candidate’s supporters to also support them without trying to argue that the other candidate is inferior.

IRV and Condorcet methods incentivize “Vote for her too” positive campaigning the most since there is approximately (or exactly) no disadvantage to candidates in saying, “Rank this other candidate second”. STAR and Approval also encourage this to a lesser extent since two candidates can mutually benefit from each of their supporters being told to give the other one 4 or 5 stars (under STAR voting) or to vote for both of them (under Approval). Even without such reciprocity, it can be advantageous for candidates in a STAR election to suggest giving certain rivals a 1 or a 2 since this makes the candidate appear less self-centered and more respectful of others at a relatively low cost. However, the STAR, and particularly with Approval, additional support for a rival may mean finishing in second place to that rival (under Approval Voting) or being edged out of the runoff by that rival (under STAR), so such endorsements of rivals are more costly than under Condorcet methods or IRV.

While IRV is great in terms of “Vote for her too” positive campaigning, it does the least of these voting methods to promote “Vote for me too” positive campaigning, since convincing a voter to rank you 3rd instead of 4th is less valuable than convincing a voter to rank you 1st instead of 2nd; it’s possible a voter’s first choice would advance all the way to the final round, in which case all of their later preferences would be irrelevant. However, it’s hard to say how Condorcet, Approval, and STAR compare in this regard. It’s presumably easier to convince a voter to give you 1 star instead of 0 under STAR Voting than to convince a voter to vote for you instead of not voting for you under Approval, but the latter is far more valuable and it’s nigh impossible to predict which results in the stronger incentive. Condorcet clearly outperforms IRV here, but again, it’s hard to predict how it would compare to Approval or STAR.

On balance, my best guess is that Condorcet methods are the best in terms of fostering more positive campaigns, followed (much more speculatively) by STAR, IRV, and finally Approval. But the uncertainty is enormous, and they should all outperform Plurality.

If reducing the importance of “electability” is important, every non-Plurality methods should offer a dramatic improvement. But IRV would probably offer the smallest of these dramatic improvements since it can be strategically optimal to rank a broadly acceptable candidate over your sincere favorite if you think there may be a center squeeze. (Imagine, for example, Democrats who loved Pete Buttigieg in the 2020 primary but voted for Biden instead because they didn’t think the country was ready to elect a gay man even if the Democratic party was. Since having a single IRV election can mimic partisan primaries, such Democratic voters would also be inclined to dishonestly rank Biden first under IRV.)

If voters support a larger fraction of women/minorities when supporting more candidates, STAR and Condorcet methods should do the best. STAR encourages voters to show some non-zero to a large number of candidates, and it often makes sense to give three or more candidates at least 4 stars. Condorcet methods reward voters for ranking all the candidates, and the lower rankings are more important under Condorcet than under IRV. Under Approval Voting, many voters will vote for only one or two candidates, so such effects should not be expected to apply to these voters.

While we can make a few educated guesses as to which of these voting methods will do the best, the most important takeaway is that we have massive uncertainty. Faced with this uncertainty, the most effective course of action for activists looking to increase the diversity of city councils and legislative bodies isn’t to pick the apparently-best of these voting methods and double down on it, it’s to get as many of these voting methods adopted in various places so that we’ll get the data to make informed decisions. This will take a lot of data, and therefore a lot of time, but the value of information is nonetheless greater than the marginal benefit of choosing what seems like the one best voting method right now.

Next post in this series: Proportional Representation



Marcus Ogren

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