PR in a Nutshell


Proportional representation (PR), especially its single transferable vote (STV), has a reputation for being hard to explain and understand. Not so. In just a few minutes, we’ll explain (and you’ll understand) how both party-list PR and STV work, and how they compare to a “normal” (in the US at least) plurality election.


The Classic Jazz Appreciation Society is planning its annual awards dinner, and our 50 members want to vote on the music program. We’ll choose ten songs, and we’d like the selection to reflect the preferences of our members, in proportion to the share of members that prefer different jazz styles.

We’re a diverse group, with fans of big-band swing, bebop, Dixieland and ragtime. Ideally, we’d like to give each member their own selection, but the dinner is only two hours long, and we’ve got speeches to give and awards to present, so our 50 members must together choose ten songs.

Our members, if pressed, would list their favorite jazz style thus:

20 prefer swing,
15 prefer bebop,
10 prefer Dixieland, and
5 prefer ragtime.

Within those groups, of course, we have different individual preferences for different composers, performers and periods, so we’ll need to find some common ground.

To begin, we’ll take nominations. For our example, let’s assume that we start with a list of 30 nominated songs, which we need to narrow down, by voting, to ten.

Multi-member Plurality

In California, most elections of this sort are multi-member plurality, and it’s the method most of us probably think of when we decide to “vote on it”. In our example, each member gets a ballot listing the 30 nominated songs, with instructions to “vote for up to ten songs.” The ten songs with the most votes win.

What happens? Well, our 20 swing fans vote for the swing songs, and even though they’re in a minority, no other song manages to get 20 votes, so we end up with an all-swing dinner. Great for the swing fans, but not ideal for the other 60% of the membership. Even if we had an actual majority of swing fans, we’d still end up with a lot of unrepresented members at the dinner, and that’s not what we want.

Proportional Representation

Our members are considerate and pluralistic, and we’d like to find a fairer way to choose the dinner music. Enter proportional representation.

PR comes in two basic variations: party list and single transferable vote, or STV. Here’s how they work.

Party-List PR

For a party-list election, we need parties—alliances of voters with shared interests. In our case, we’ll have a party for each jazz style. Each party nominates its own songs and puts them on a list, so we end up with four lists: swing, bebop, Dixieland and ragtime. The members of each party decide which songs to put on the list, and in which order. If they can’t agree, they’re free to form new parties (we could have a separate Glenn Miller party, for example), but for now, we’ve got four.

In the election, each member votes for a list. If the swing list gets 20 votes (as we might expect), that’s 40% of the vote, which entitles the swing party to the first four songs on their list (40% of the ten songs to be chosen). Similarly, the bebop fans get the first three songs on their list, and so on.

If a party is too small, it’s not going to have enough votes to win a place on the program; we only have time for ten songs.

This is pretty good, but it’s not perfect. For example, a swing fan might be fine with the Benny Goodman as their first choice but might prefer a little bebop to Big Bad Voodoo Daddy, thank you very much. Problem is, members have no way to show preferences for individual songs or to split their vote between the swing and bebop parties.

Enter STV.

STV PR in Two Minutes

First, we tack 30 sheets of paper to the wall, each with the name of one of the 30 candidate songs. We ask each of our members to stand by the sheet with their favorite song. With 50 voters, and ten songs to be chosen, a song will need at least five votes to win a place on the program.

Once we have ten songs, each with five members voting for it, we’re done. It’s easy to see that each of the styles can win its fair share of the program.

But at first, we’re not likely to have exactly ten groups of five voters. Some songs will have more than five votes, and others fewer. So, if a song has more than five voters, the surplus voters are asked to go and stand by their next choice (one without five votes yet), until no song has more than five votes—though several might still have fewer.

We then eliminate the song with the fewest members voting for it, and ask those members to go stand by their next-favorite song that’s still not elected. We continue until we have ten songs each with five votes, and we’re done.

This might be just a little messy for 50 voters, 30 candidates, and ten songs to be chosen (or seats to be filled); certainly for bigger groups, or for groups who aren’t all in one room at one time, it’s just not practical.

STV solves the problem by asking the voters to list their songs in order of preference on a ballot. We first award each ballot to its top-choice song. Songs that have more than five votes send their surplus votes to second and lower choices. Then songs with the least votes are eliminated, one by one, sending their ballots on to the second and lower choices, until we have ten songs with five votes each.

And that’s it. Simple as S-T-V.


This is just how early STV systems worked. Modern STV systems use the same principle but refine the procedure a little. For example, if a song has ten votes, which five voters get to go vote for their next choice? What do we do when we have a tie? What if the numbers don’t work out as neatly as in our example? What if voters don’t rank all the songs?

All those questions have good answers, but they’re not essential to understanding the principle by which STV gives us proportional results.

One last thing. Notice that in the STV election, each of the 50 club members ends up contributing to the selection of a song. That’s the ultimate aim of proportional representation: to give every voter a voice in the result.

Frequent Questions

Why is it called “single transferable vote”?

Single: each voter has a one vote.

Transferable: a vote can be transferred, from a winning candidate with too many votes, or from a losing (eliminated) candidate, to the next preference listed on the ballot.

Why are STV surpluses transferred? Why are they transferred before eliminations?

Suppose, in our example election, our 10 Dixieland fans (who should be able to choose two of the final songs) all rank “Basin Street Blues” first, and “When the Saints Go Marching In” second. If we didn’t transfer surpluses first, “Saints” would immediately be eliminated, with zero first-choice votes. But that’s wrong, since this group of voters should be entitled to their first two choices. We achieve that by transferring surpluses as soon as they arise.

How are STV surpluses transferred fairly?

When we discussed surplus transfers in the example, it seemed a little unfair, in that voters who got to move to their second choice seemed to get a free ride on their first choice. This problem is generally solved in one of two ways.

The first way is to choose the voters whose ballots are transferred at random. This is fair in two respects. First, each voter has the same choice of being chosen for the transfer. Second, in large elections, the voters chosen at random will be a representative sample of all the voters in the group. So even if my ballot isn’t chosen, another ballot similar to mine will be, at least at a high statistical probability.

The second way is now more common, and is used in most public STV elections. Take the Dixieland example again, with ten first-choice for “Basin Street Blues,” where only five votes are needed to win. We allocate half of each vote to “Basin Street Blues,” leaving it with the required five votes, and then transfer the balance of each vote (in this case, the other half) to the second choice. We make a similar calculation each time a surplus is transferred. (Notice that each voter still has only one vote, but that vote can be spread over multiple candidates.)

What are all those terms and acronyms?

Here’s a summary.

STV is the “single transferable vote,” the system we described above. It’s sometimes called “choice voting,” or even “full-choice voting.”

When STV is used for single-seat elections, it’s known as the alternative vote (AV), or, in the US, as instant runoff voting (IRV). In the single-seat case, no surplus transfers are required. The multiple-seat version of STV is sometimes called STV-PR (or PR-STV), emphasizing that it’s a form of proportional representation.

Ranked-choice voting (RCV) is another name for all the above forms of STV. There are voting systems besides STV in which voters rank candidates, and RCV or “ranked voting” can include them as well, depending on the context.

“Surplus votes” are the votes a winning candidates receives beyond the number required for election. If five votes are required for election, a candidate receiving seven votes has a surplus of two votes. The surplus votes are transferred to the next choice on the ballots.

How do nominations work?

One possibility: any member can nominate five songs, and any song that gets five nominations makes the list of candidates, so even the smallest of our groups, the ragtime fans, can nominate five songs. For this election, we ended up with 30 nominated songs, which we need to narrow to ten, by voting.


Leave a Reply

Your email address will not be published. Required fields are marked *