While Congress has twice mandated the use of single-member districts (SMD) for electing members of Congress (once in 1842 and again in 1967), state legislatures are at liberty to determine how their representatives will be elected.

According to FairVote, at one time, more than half of all state legislators were elected from multi-member districts (MMD). Fifty years ago, more than two-thirds of states had at least some multi-member districts.

Today, that number has dropped to just ten: Vermont and West Virginia use MMD for both houses in their state legislatures, while Arizona, Idaho, Maryland, New Hampshire, New Jersey, North Dakota, South Dakota, and Washington state use MMD in their lower houses only.

Writing for

Stateline in 2011, Josh Goodman noted that the Voting Rights Act (VRA) was a major reason for the substitution of multi-member districts with single-member districts. Since MMD systems tend to require larger districts, Goodman observed, they "make it harder to create constituencies where minority groups are concentrated enough to elect candidates of their choice."

Indeed, in 1986, the U.S. Supreme Court ruled in Thornburg v. Gingles that North Carolina's MMD legislative lines were discriminatory toward blacks, and to avoid VRA lawsuits, states started to move toward SMD systems.

As of August 2015, according to Ballotpedia, 1,082 of the country's 7,383 state legislators were elected from multi-member districts – just 14.7%.

Yet given the level of mistrust that Americans have for public institutions today, it is worth examining whether multi-member districts live up to one of their primary promises – that is, to allow voters to send multiple representatives from their district to the state capitol and to have that multi-member delegation reflect the diversity of the district in a way that is impossible with just a single representative.

First, it is important to differentiate the way states today implement MMD from how many countries use proportional representation (PR).

In today's state legislatures, voters in most cases vote for candidates equal to the size of the district's magnitude (that is, how many lawmakers represent it) – a method of voting called "bloc" voting.

In some states, the magnitude is fixed and equal across all districts. In New Jersey, for instance, when selecting representatives to the General Assembly, voters pick two candidates to represent their district, and the top two vote-getters in each district win.

In other states, the magnitude depends on the size of the district. In New Hampshire, for instance, districts for the state House of Representatives have a magnitude between 1 and 11. In Hillsborough-37, the state's largest district, voters in the general election choose 11 different candidates.

In many PR systems, on the other hand, voters select not individual candidates but instead vote for political parties, and then party members fill seats in proportion to each party's electoral performance. For instance, in theory, a party that wins 35 percent of the vote will claim 35 percent of the seats in the legislature.

So, with this information, we can now ask, how well does the MMD system work in these 10 states? How well do representatives from such districts reflect the diversity of their constituents?

Based on my research, there are 471 multi-member districts in these ten states. Among these districts, 89 of them have representatives from more than one party. This works out to 18.9 percent. (In my tabulation, I discounted a district in which all representatives are of the same party, yet at least one of these representatives is also the nominee of a minor party – such as if Representative A were a Democrat, and Representative B were a Democrat who also ran on the Work Families Party line).

However, this figure is not entirely accurate for our purposes. In West Virginia's state Senate, for instance, the two senators in each district are elected on a "staggered" basis, such that one senator is elected in one cycle and the second senator is elected in another cycle.

In other cases, such as Idaho's state House, representatives from each two-member district are elected to separate "posts" – such as 1A and 1B – and thus they also never square off competitively.

When these non-competitive elections within multi-member districts are removed, the number changes slightly: in the remaining 368 multi-member districts in which representatives are elected concurrently, 77 are served by members of more than one party – amounting to 20.9 percent.

One example of such a district is District 51 for West Virginia's House of Delegates: with five members, it is the state's largest district by magnitude.

There, in 2014, voters ousted two Democratic incumbents and replaced them with two new Republicans -- they also re-elected two Republican incumbents. However, instead of electing Republican candidate Bill Flanigan in a straight-ticket fashion, they re-elected Democratic incumbent Barbara Evans Fleischauer. The district is thus represented by four Republicans and one Democrat.

Ten of the 20 multi-member districts in West Virginia's lower house are represented by more than one party.

Another district with multi-party representation is Chittenden, the largest senate district in Vermont with a magnitude of six. In 2014, voters from this largely "liberal" district sent a diverse delegation to the capitol that included three Democrats, two Democrats who also appeared on the Vermont Progressive Party line, and one Republican, Diane Snelling.

With over 21,000 votes, Snelling defeated Democratic candidate Dawn Ellis by more than 3,000 votes – a sign that Chittenden voters are also not knee-jerk, straight-ticket partisan voters.

Nevertheless, just three of the 10 multi-member districts in Vermont's upper chamber are represented by members of more than one party. The multi-member districts of Addison, Bennington, Essex-Orleans, Windham, and Windsor are represented exclusively by Democrats, and the multi-member districts of Franklin and Rutland are represented exclusively by Republicans.

It is this kind of outcome that caused Steve Hingtgen, a member of Vermont's Legislative Apportionment Board, to fret in 2011 that, “Larger districts in Vermont are a way for majorities to prevent regional minorities from winning seats.”

Nowhere is this regional party-dominance more apparent than in Hillsborough-37, the 11-member district in New Hampshire. This district is currently represented by 11 Republicans, despite the Democratic candidates receiving 28.5 percent of the vote in 2014.

Of the 99 multi-member districts for New Hampshire's lower house, 74 are controlled by a single party.

According to FairVote, the problem with bloc voting – in which voters cast ballots equal to the district's magnitude – is that it is, like voting in a single-member district, essentially a winner-take-all system. As seen in the case of Hillsborough-37, a political majority can keep a political minority off the ballot if they vote as, well, a bloc.

FairVote suggests combining multi-member districts with other measures, such as ranked choice voting, to prevent such monopolistic outcomes. To produce a more representative system, it proposes a candidate-centric model that it calls "fair representation voting."

Nevertheless, one way in which the MMD system, even in its current form, has improved representation is in terms of allowing women to get elected to office.

In January 2014, women comprised 31 of the chambers that used multi-member districts, whereas women comprised 22.8 percent of the chambers using single-member districts.

In some cases, the presence of women on the ballot can cause voters to buck their partisan voting habits. In New Hampshire in 2012, for instance, voters in Rockingham-6, a 10-seat district that leans heavily Republican, elected two Democratic women – Elizabeth Burtis and Mary Till – over two Republican men to round out an otherwise all-Republican delegation.

Researchers Jennifer Hayes Clark and Veronica Caro, studying the use of multi-member districts in Arizona's lower house, found that bloc voting benefits women because it incentivizes them to distinguish themselves from other candidates on a crowded ballot and even to create intra-party competition. They also found that, once elected, women speak to and legislate on behalf of women's issues that otherwise might be neglected, often crossing the aisle to do so:

...when we examine legislators’ propensity to cosponsor together based on demographic and partisan variables, we see a strong relationship emerge among female legislators, in which women are much more likely to cosponsor legislation concerning women’s issues with one another, especially in bipartisan fashion. This effect is present even after controlling for the effect of ideology but is unique to women’s issues.

In short, the use of multi-member districts does affect representation in several state legislatures. Where there are competitive elections for multiple seats in a single district-wide election, more than one-fifth of these districts see representation by more than one party. Also, under the MMD system, women see substantial gains in their electoral performance.

However, these elections are fundamentally similar to single-member districts in that they are winner-take-all elections: since voters select candidates equal to the district's magnitude, it is possible for a political majority to prevent the election of even a single candidate from the political minority if the majority votes as a bloc.

With the adoption of additional measures, such as ranked choice voting, the MMD system could further improve representation in state legislatures all across the country and (dare one even suggest it?) in Congress itself.