A proportional representation PRimer

How to end Gerrymandering

If, like most native English speakers, you live in a country that uses single-member districts, it may seem as if that’s the only way to do things. But in reality, over 60% of democracies include some form of proportional representation (PR) in their electoral system for choosing legislators. That means systems where a group which gets X% of the votes is guaranteed to get within some small rounding error of X% of the seats. In other words, unlike the system you’re probably used to, one where you can’t turn 40% of the votes into 60% of the seats just by “gerrymandering” some lines.

A visual explanation of gerrymandering, showing how 40% of the voters can get anywhere from 0% to 60% of the seats, depending how districts are drawn.

Ideally, PR is a way for the voters to naturally self-organize into coherent voting blocs like the vertical stripes above, without anybody having to draw the lines for them. And it would solve more than just gerrymandering. By allowing candidates to compete to represent all the voters and not just the partisan primary electorate and the deep-pockets donors, it would hopefully reduce polarization and enrich the debate.

There are various types of PR voting methods. Historically, designing PR methods has involved tradeoffs between competing goals such as ballot simplicity versus voter power. However, the newest, best methods can mostly transcend such tradeoffs.

Existing PR methods

Multi-member districts with Single Transferable Vote (STV)

This method is good at holding candidates accountable and has reasonably simple ballots, but allows a greater margin for disproportionality than most other PR methods. Instead of having just one “at-large” (nationwide or statewide) election, there are several separate regional “district” elections, typically for 3–7 seats each. Within each district, voters rank all the candidates in order of preference; the weakest candidates are eliminated and their supporters’ votes are transferred until a proportional result is found.

Transferable methods are part of the voting system in countries like Australia and India.

Party list methods

These methods are great for ballot simplicity, but are not the best for individual voter power. The basic idea is that proportionality is tallied only at the party level; the number of votes for each party are counted, the party is assigned a proportional number of seats, and only then are the seats assigned within the party. They are divided into closed list systems, in which voters only choose a party, and the party itself decides how to allocate its seats; and open list systems, in which voters also choose a candidate by name, and the seats are allocated to the candidates with the most votes. Of these two subtypes, open list systems are clearly a better way to avoid corruption.

Party list methods of some form are the basis of the legislative electoral systems of 68 countries.

Mixed member methods:

These methods (sometimes called MMP, for mixed-member proportional) do well at geographic representation, ballot simplicity, and precise proportionality, at the cost of some complexity in the counting process and reduction in individual voter’s power to support subfactions within their overall party. The idea is that some portion of the seats are elected by single-member districts, but a party-list procedure is then used to “top up” each party to the correct proportionality. Procedures for actually doing this can be complex, and if there are not enough “extra” seats then certain parties, especially smaller ones, may get more than their proportional share.

Mixed member methods or the related “parallel” methods are used in the electoral systems of 28 countries.

Newer methods and add-ons

The methods above are widely-used, but they have some disadvantages. Newer voting method designs make it possible to minimize these disadvantages.

Delegation

STV, described above, is good at keeping representatives individually accountable. But it requires voters to do a fair amount of work to rank all the candidates in preference order. If voters don’t want to spend all that time, they can delegate: let somebody else do that job for them. Here’s who voters could delegate to, and how the system would enable that:

Parties . Each party has a public predefined preference order, and voters have a simple way of choosing that order. In Australia this is called “above-the-line” voting. While this simplifies the voters’ task, it also has some of the disadvantages of closed party list methods, in that it opens the door for party wheeler-dealers to entrench themselves and become unaccountable to voters.

. Each party has a public predefined preference order, and voters have a simple way of choosing that order. In Australia this is called “above-the-line” voting. While this simplifies the voters’ task, it also has some of the disadvantages of closed party list methods, in that it opens the door for party wheeler-dealers to entrench themselves and become unaccountable to voters. Candidates. As above, but each candidate within the party has a different predeclared preference order. This gives the voter more power to choose between the various ideological sub-factions of their preferred party.

As above, but each candidate within the party has a different predeclared preference order. This gives the voter more power to choose between the various ideological sub-factions of their preferred party. Other same-party voters. When your top preference is eliminated, your vote is split among all the candidates for that same party, in proportion to the number of voters who chose them as a top choice. Just as “above-the-line” delegation would reduce to closed party list if everyone did it, this “voter delegation” would reduce to open party list if everyone did it. But unlike party list methods, using STV still means that highly-engaged voters have the power to choose their own preference order.

District-specific ballots

Another way to simplify ballots is to only explicitly list the candidates running in the local district, but still allow voters to write in candidates from elsewhere. This blends the voter freedom of at-large elections with the “local feel” of mixed-member or multi-member methods. (As far as I know, this idea is still not used in any country.)

Minimum quotas

In some places, proportional methods have been criticized for leading to too many small parties, so that building majority coalitions to form a parliamentary government becomes impractical, and tiny one-issue parties wield outsized power in such coalitions by threatening to vote against key legislation. So some electoral systems include rules to encourage larger parties that are a product of pre-election coalition building between smaller interest groups, rather than tiny parties focusing on only one small group or issue.

In party list or mixed member methods, this is often dealt with through minimum party quotas; for instance, in Germany, parties with less than 5% of the votes and fewer than 3 district seats get no proportional seats. This means that the proportional part of the vote for such parties is ignored. In transferable vote systems, it would be possible to similarly discourage splinter parties with a minimum preferred support quota rule: candidates who are the first choice of a small enough group are eliminated before they have a chance to receive any transferred votes.

Overlapping territories

Though the nonproportional “First Past The Post” system is terrible in many ways, it does have one advantage: each voter could find and point to “their” representative, the politician responsible for listening to their concerns. To make this possible with PR, parties can assign their elected representatives territories, so that each location is in the territory of one representative per winning party. Thus the territories for a given party would be smaller in places where that party’s voters were a concentrated majority, and larger where they were a more spread out minority. This would not just keep direct personal responsibility, it would improve it: even if your party is a minority in your area, you’d have your own sympathetic representative whom you’d helped elect.

Geographic constraints

In some places, overlapping territories are not enough; there is a legal requirement to elect exactly one candidate per area (district, riding, or constituency). In that case, there can be rules to ensure that this happens. This makes things slightly less proportional and gives voters slightly less ability to hold individual politicians accountable.

Putting it all together: the OL/D voting method

If you start with at-large STV and use most of the add-ons above, you get OL/D voting, a method designed to give all the advantages of PR without giving up any of those of first past the post. Here’s a quick summary of the steps of this method:

The area is divided into one equal-population district per seat. However, the exact lines are not so important, as they’re only used for simplifying the ballot.

Ballots list the local district candidates, and voters can either choose one or write in somebody from farther off.

Voters also choose whether to trust the other same-party voters (default) or to delegate their ballot to their chosen candidate’s predeclared preference order.

Candidates with less than 25% of a district of votes are eliminated (unless they’re in the top two for their district)

Find winners using STV

Each district is assigned to the territory of one representative per winning party, so that representatives typically have multi-district territories (overlapping between parties, separate within parties). For instance:

Here’s the real-world results for congressional races in Tennessee 2016. Gerrymandering favors the Republicans here; they get 78% of the seats with only 63% of the vote. With PR, it would have been 6R, 3D…

…each of the 6 Republican winners would have gotten a territory of 1 or 2 districts…

…while the 3 Democrats would have gotten territories from 2 districts (near D stronghold Memphis) to 4 districts (in the eastern part of the state where there are fewer Democrats per district). Note that the gerrymandered districts have not been redrawn, but they cease to help either party.

OL/D combines various tricks to give a good method when most candidates belong to parties. It’s also possible to use similar tricks for a proportional nonpartisan method.

Is reform feasible?

In the Canada and the UK, the movements supporting PR are growing stronger. Though the US isn’t quite as far along, it’s not as hard as most people think. Changing the electoral system can be done mainly at the local and state level, with no constitutional amendments. The only federal law getting in the way of state-by-state reform is one clause that was tacked on to a 1967 law giving citizenship to one man in L.A. Remember, the US has reformed and improved its election systems many times in the past, and we can do it again.

And remember why we’re talking about this in the first place: gerrymandering. The people are ready for solutions to corruption and polarization. PR won’t solve all the problems, but it will clearly help.

Proportional representation kills the Gerrymander

Further resources

BEST voting method picker tool: for finding a good voting method based on the user’s priorities. Unfortunately, it doesn’t include any of the newer methods and add-ons listed above.

FairVote has a library of links about PR. (Note: FairVote is not as good as Electology.org for single-winner voting methods, but they still do good work, especially on proportional representation.)

A note on terminology: “Electoral system” means all the election rules of a given country, including voter and candidate eligibility, elections for different offices, campaign rules, etc. “Voting method” is the formal mathematical part of that; the algorithm that determines what information must go on each ballot and how that information is aggregated to choose a winner. I’ve avoided the term “voting system” because it’s ambiguous; it could refer to either of the above, or to the specific machines used for casting ballots.