Single Transferable Vote PR

Unlike party-list PR, Single Transferable Vote PR (STV PR) does not rely on parties. While STV can be (and is) used in partisan elections, it is also suitable for non-partisan elections, and is the only fully proportional system in use for that purpose. This makes STV especially useful for non-partisan elections such as those for city councils and school boards.

While Single Transferable Vote (STV) comprises a family of variations, the underlying method is the same:

  • Ranked ballot. Each voter ranks some or all of the candidates in order of preference.
  • Establish quota. The quota is the threshold number of votes required to elect a candidate.
  • Elect winners. The first choices of all the ballots are tallied, and the candidates receiving at least a quota of votes are elected.
  • Finished? If the number of candidates remaining is equal to or less than the number of unfilled seats, the remaining candidates are elected. If all seats are filled, or no candidates remain, the count is complete.
  • Transfer surplus. If seats remain to be filled, transfer votes received by elected candidates in excess of the quota to the next choice on the ballots, and resume the process with Elect winners.
  • Defeat low candidate. After all surpluses have been transferred, if seats remain to be filled, defeat (eliminate) the candidate with the fewest first-place votes, and transfer that candidate’s ballots to the next candidate listed on each of those ballots. Continue at Elect winners.

Eventually, either all seats will be filled or all candidates will be elected.

Each voter has a single vote (hence the name “single transferable vote”), which is eventually counted toward one of the candidates (or, in some STV methods, divided among multiple candidates). All or part of a vote can be non-transferable and not counted if the ballot, for example, ranks only candidates who have been defeated.

Evolution of STV methods

Specific STV methods vary in how arithmetic is performed (precision and rounding), how the quota is calculated, and how ties are treated (ties can arise in Elect winners and Defeat low candidate). Most important, STV methods differ in the manner in which they transfer surplus votes from elected candidates to still-hopeful candidates. Elsewhere, we discuss the evolution STV variations in a historical context, looking at how increasingly sophisticated methods have been developed. This evolution was a consequence of a better understanding of the mathematics of election methods, along with the availability of calculators and computers to aid vote counting.

STV in a Nutshell

Hoag & Hallett (1926) offered perhaps the simplest-ever set of instructions for an election that gets at the basic idea of STV. They ask us to imagine the election of a five-member council, carried out in a park. Nine candidates have been nominated. Here are the rules:

  1. To vote, stand beside the banner of the candidate who you prefer.
  2. Change your vote as many times as you please until the polls close.
  3. When the polls close, the five candidate who are surrounded by the five largest groups of voters will be declared elected.

The basis of STV lies in the recognition that voters who stand by a candidate with very few votes are motivated to move and help elect their second choice, and that a candidate with more than 1/6 of the votes can’t lose, so any votes beyond that are also free to help elect their second choice.

For more complete, but only slightly more complicated, description of the principles behind STV, see STV in a Nutshell.

Why Use STV PR?

Given that proportional representation is desired, why would we choose the STV form of PR?

STV PR vs List PR

When proportional representation is a requirement for a non-partisan election, STV PR is an easy choice over list PR, because there are typically no entities (most often parties) to create the candidate lists required for list PR. We see this in Cambridge MA and Minneapolis MN, where STV PR is used for non-partisan municipal elections.

STV PR can also be used for partisan elections. While we don’t have an example of partisan STV elections in the US, the Irish lower house of Parliament, Dáil Éireann, has been elected with STV since 1922.

STV PR vs Semi-Proportional Methods

When proportional representation is required, we can dispense with such majority-take-all systems such as plurality-at-large, and approval voting, or single-member districts with any voting method.

We do, however, sometimes see semi-proportional voting methods, most often cumulative voting or single non-transferable vote (SNTV), proposed. It’s useful to understand why such methods are much less satisfactory than STV PR for delivering proportional results.

We apply the term “semi-proportional” to voting methods in which a minority can achieve some measure of representation through voting power, but where full proportionality is not guaranteed. The lack of full proportionality can be due to the absence of fully proportional voting power, or, more likely, an implicit requirement that a voting bloc perfectly coordinate their votes in order to achieve full proportionality.

See Semi-proportional Electoral Methods for a discussion of the problems of those methods.


4 Responses to STV PR

  1. jshannon says:

    It looks like the “STV PR” and “List PR” tabs contain the same language.

    It seems like the process of “Find Winners” is used interchangeably with “Elect Winners.”

    Might be helpful to describe which transfer votes from a winning candidate are transferred to another candidate. For example, if the threshold quota is 15% and Candidate A gets 20% of the first place votes, which votes make up the 5% transferred?

  2. jlundell says:

    Thanks, Jim. Fixed. (And I’d be grateful for any other corrections.)

    I’ll look at revising the mention of surplus transfer in the Evolution paragraph. It’s only a small oversimplification to say that the entire considerable history of STV methods revolves around deciding the question of how to transfer surplus votes. The other differences are relatively minor, and I should make that clearer.

    I’m convincing myself that this subject deserves explicit attention on the evolution-of-STV page.

  3. icr says:

    STV failed miserably when it was voted on in British Columbia because
    of ads like this:

    There is no reason to think that the results would be any different if STV were to be put to the test in any US state with initiative and referendum. In states without i&R it would be a long shot-duopoly pols have a natural resistance to putting their jobs at risk.

    Open list PR (e.g. Finland) is a simpler and far more widely used system that should be an easier sell-especially combined with easy ballot access for new parties.
    It’s a natural proposal in the 49 of 50 states with bicameral legislatures. Since the SCOTUS “one man, one vote” decisions of the early ’60’s these states have been electing mirror-image houses in elections that normally result in interchangeable D or R party bosses running each house. Electing one house by open list PR with a single statewide district (or a handful of districts) would allow for a wider number of ideological and other interests to represented in government. To understand what I’m getting at think of Illinois, where a bipartisan corrupt “combine” (see John Kass, Chicago Tribune) with links to organized crime has been running state government as more or less a private hunting preserve for decades.

    P.S. STV again: it takes too much ‘splainin’ to address charges like these:
    STV’s complicated voting system means your single vote will be fractionalized and distributed so that you may never know how it was counted. You can mark your preferences but you have no control over what part of your single vote gets distributed to any of your preferences.

    STV supporters use the analogy of your vote being like a dollar and you decide to spend it on several candidates, but that is misleading because STV does not allow you to determine whether your first preference gets 50 cents, 10 cents or nothing at all. How much is spent on each candidate depends entirely on how the vote count unfolds.

    Those who vote for sure losers, like the Work Less Party, get to have their vote transferred at full value to their second choice, but those who cast a serious vote have their second preference count for a small fraction of a vote. What’s fair about giving sure losers a second vote and serious voters a small fraction?

  4. jlundell says:

    icr’s comment on resistance to change is an important one, and we should note that it extends beyond party pols, STV and PR. In San Mateo County (CA), the nominally non-partisan Board of Supervisors voted down 4-1 a proposal from their own Charter Review Committee to put district elections for the Board (vs the current at-large elections) on the ballot. Their view, frankly expressed, was that there really couldn’t be anything wrong with a system that had managed to elect such fine specimens as themselves.

    I do think that STV has a decent chance in the near term for local elections, especially where (as in California) they’re non-partisan, no-primary elections. I’m not sure that a party-list proposal for statewide elections would get much farther than STV.

    I’m intrigued by the example of Norway (described briefly elsewhere on this site). It’s nominally a closed list, but non-party (or minor-party) entities can put forward their own list by petition. Open, but in a different and perhaps more useful way.

    At any rate, the mission of this site is primarily education, with a focus first on PR per se, and only secondarily on the mechanism my which it’s achieved.

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