For much of the 1980s, Wyoming had more women serving in its state legislature than almost all other states, living up to its nickname: the Equality State. Today, Wyoming ranks 48th, up from dead last in 2018.

It’s difficult to point to a single reason why so much changed in Wyoming. Yes, Wyoming has become more conservative, and the number of female politicians in the Republican Party has been stagnant or declining for years. But something else happened in Wyoming that may have inadvertently slowed the state’s momentum when it came to electing women to political office: the state changed how people are elected to political office. In 1992, the Wyoming state legislature switched from multi-member districts — when voters elect multiple people to represent their district — to single-member districts — when voters elect one person to represent their district.

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It may seem like an innocuous change: If women were likely to be elected in one system, then they should be in the other. But there’s a host of research suggesting that in multi-member districts, more women might be encouraged to run and more women might win. For a country that still elects three times more men than women to state legislatures, multi-member districts might be a simple trick to help balance the scales — if only it weren’t going out of style.

Political scientists have spent a lot of time examining what increases the likelihood of a woman running and getting elected. We hear about how women need to be recruited, how they need deeper political networks and support. But the structure of elections may also shape women’s electoral fortunes in profound ways.

To understand why, we’re going to need to wade into the depths of political science jargon and learn about something called district magnitude. District magnitude refers to the number of candidates elected from a specific political district. These decisions are made at the state level every 10 years. In multi-member districts, voters vote for two or more candidates to represent their district. These representatives then split duties, like two U.S. senators from any given state do. District magnitude varies across, and even within, states. When electing representatives to New Hampshire’s lower chamber, for instance, voters select between one and 11 candidates, depending on the district.

Multi-member districts are increasingly rare, though. The number of states that have at least one legislative chamber with multi-member districts has steadily declined, from 39 states in the 1950s to 17 states in the ’80s to just 10 states today.

This matters for women’s representation because some research has suggested that district magnitude can influence both the supply of and demand for female candidates. Though women are generally less likely to be recruited to run for office, parties in states with multi-member districts may feel more pressure to balance their list of candidates in an effort to appeal to a wider range of voters. As University of Kentucky political scientist Tiffany Barnes explained, “Whereas access to the ballot is a zero-sum game in single-member districts, in multi-member districts multiple candidates — from the same political party — can occupy a place on the ballot.” And other political scientists have suggested that parties and voters may be more willing to support a woman when she is not the only possible candidate, in part because of bias against female candidates.

Multi-member districts also see more turnover, which may create more opportunities for women to run and fewer contests against strong incumbents. (Turnover presents similar conditions to term-limited seats, which might also increase the number of female candidates.)

Multi-member districts may also change the kind of campaign that candidates need to run, often in ways that could be helpful to women. Although races in multi-member districts generally include more opponents, candidates running for a seat in a multi-member district spend less time attacking each other and more time promoting themselves. As political scientists Michael Horan and James King explained in a 1999 study examining the elimination of multi-member districts in Wyoming, “The typical head-to-head battle between a Republican and a Democrat is replaced by something of a free-for-all where each candidate emphasizes his/her own strengths rather than his/her opponent’s weaknesses.” This free-for-all, they said, can alleviate reservations about facing a contentious campaign period, which may encourage more women to run.

So if more women are elected in multi-member districts, why are they disappearing?

Legal battles have a lot to do with it. Wyoming eliminated its multi-member districts after a federal court ruled that these districts violated the Constitution by distributing the population in a lopsided way. Other states eliminated their multi-member districts after the Voting Rights Act of 1965 opened the door for judicial review of electoral practices that discriminate against racial minorities. Numerous court cases have debated whether multi-member districts dilute the value of votes cast by racial minorities and some rulings have invalidated their use, which might have inadvertently made it harder for women to get elected, at least for a while.

Take North Carolina, which phased out its multi-member districts over several decades in response to such a legal challenge. In the 1970s, more than 80 percent of the seats in the state legislature were in multi-member districts. That dropped to around 60 percent in the 1980s, and around 30 percent in the 1990s. As the number of multi-member districts declined, so did North Carolina’s national ranking with regard to women’s representation. (However, the state saw its ranking improve between 2004 and 2008, after Democrats gained control of both legislative chambers, but it was short-lived — today the state is ranked just 33rd.)

But although multi-member districts have gotten a lot of blame for watering down the power of racial minorities’ votes, those challenges exist no matter how districts are structured: Single-member districting arrangements have seen their share of legal battles, too. And academic studies find that single-member districts don’t often give an advantage to minority candidates — in fact, they might even put women of color at a disadvantage.

While more women are elected in places in which district magnitude is larger, there are of course other factors that are also correlated with women being elected. For instance, in a recent study, political scientists Nicholas Pyeatt and Alixandra Yanus identify a dozen attributes characteristic of “women-friendly districts,” such as liberal, urban, racially and ethnically diverse areas, that have a history of electing women to state legislatures. In fact, as Yanus explains, “Many of the states that [still] use multi-member districts have political cultures and landscapes that we would argue are conducive to the election of women in the first place” — making it hard to isolate the effect of district magnitude alone. Untangling all these factors is something gender and politics scholars continue to work on.

But in the absence of such attributes — say, a rural county in a racially homogenous, conservative state like Wyoming — multi-member districts may have given women the leg up they needed to achieve greater representation. So while it is unlikely that Wyoming, or other states that have eliminated their multi-member districts, will bring them back, organizations and parties that want to encourage greater women’s representation might try to mimic the effects that multi-member districts enabled. They could reduce the combative nature of elections, or increase the recruitment of women. Maybe that would do the trick.

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