# STV in a Nutshell

## Introduction

The 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 STV works.

## Context

The Academy of Motion Picture Arts and Sciences has used STV for their Oscar^{®} nominations since 1936, typically nominating five candidates per category.

But suppose that the Academy, instead of having its members nominate candidates by group vote, employed a panel of five respected critics to choose the five best-picture nominees. One way to let each critic have a voice in the final selection would be to present the panel with a list of the year’s movies, and ask each of the five to choose the best one. (If two critics chose the same movie, they could flip a coin, and the winner would choose another movie not chosen by any of the other critics.) The result is fair, and the nominees will be a representative cross-section of critical opinion; different critics have different tastes, and we want a range of taste in the nominated group.

How do we achieve the same range of opinion when a larger group of Academy members are doing the nominating? A proportional representation vote.

## Vote for five?

Using the ordinary plurality voting system you might be familiar with for your local city council or school board, we could ask each member to vote for his top five picks, count up the results, and nominate the five movies with the most votes. The problem with this approach is that a majority, or often a plurality less than an actual majority, gets to pick all five nominees. This isn’t what we’re after; we want each nominee, including the fifth, to be the passionate choice of a significant portion of voters, not the fifth-place choice of the majority.

## Proportional Representation

Enter the single transferable vote, or STV. To make our example simpler, we’ll assume that we have 50 Academy members together in a room to do the nomination voting.

## STV PR in Two Minutes

First, we tack 30 movie posters to the wall, one for each of the 30 candidate movies, and ask each of our members to stand by the poster for their favorite. With 50 voters, and five movies to be chosen, a movie will need at least ten votes to win a nomination.

Once we have five movies, each with ten members voting for it, we’re done. It’s easy to see that any movie with the support of at least ten members can win a nomination.

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

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

This might be just a little messy for 50 voters, 30 candidates, and five movies 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.

In practice, STV solves this problem by asking the voters to list their movies, or candidates, in order of preference on a ballot. We first award each ballot to its top-choice move. Movies that have more than ten votes send their surplus votes to second and lower choices. Then movies with the fewest votes are eliminated, one by one, sending their ballots on to the second and lower choices, until we have five movies with ten votes each.

And that’s it. Simple as S-T-V.

## Conclusion

This is how early STV systems worked. Modern STV systems use the same principle but refine the procedure somewhat. For example, if a movie has 20 votes, which ten 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 movies?

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

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

## Frequent Questions

### What STV method does the Academy use?

The Academy does not appear to publish the details of their STV rule, but from assorted published information it appears that they use a the WIGM, or weighted inclusive Gregory method, similar to the STV rules used by Minneapolis MN and Scotland.

### 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 20 fans of blockbuster movies (who should be able to choose two of the final nominees) all rank one blockbuster first and the other second. If we didn’t transfer surpluses first, the second blockbuster 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 blockbuster example again, with 20 first-choice for blockbuster #1, where only ten votes are needed to win. We allocate half of each vote to blockbuster #1, leaving it with the required ten 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 did we get the list of candidates in the first place?

One possibility: any member can nominate five movies, and any movie that gets five such nominations makes the list of candidates, so movies with relatively low initial support can make the list. For this election, we ended up with 30 candidate movies, which we need to narrow to ten, by voting.