Single Transferable Vote

The Single Transferable Vote, or STV, is a preferential voting system designed to minimise wasted votes and provide proportional representation in multi-candidate elections while ensuring that votes are explicitly for candidates rather than party lists. STV systems achieve this by initially allocating an individual's vote to their most preferred candidate and then subsequently transferring unneeded or unused votes after candidates are either elected or eliminated according to the voter's stated preferences.

Voting

STV voting acknowledges that voters for each elected representative may prefer different unelected candidates. To ensure this, excess (unused) votes from winning and losing candidates are transferred to remaining candidates according to the voter's preferences.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This method is sometimes approximated in elections among schoolchildren; the children line-up behind the candidate of their choice until enough members have a long enough line behind them. Since the children would all know that each candidate only needs a certain number of classmates' votes to be elected, those arriving last in line for a candidate who already has enough votes would choose to not waste their vote and instead move to another line to help someone else to win. Likewise, those children whose candidate obviously could not win would move to another line, and so on, until all the representatives are chosen.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This process is automated in STV by use of the preferential ballot, a method for determining how to transfer votes, and a derived quota for determining winners. Each winning candidate represents a single quota's worth of votes analogous to the children lined up behind him, and voters are in turn automatically lined up and transferred according to how their preferences are listed on their ballots. "Wasted votes", those that go to non-winning candidates or candidates that have already won, are therefore effectively minimized in STV systems, simultaneously minimizing the number of unrepresented voters and providing a degree of proportionality. Depending on the method of STV used and the preference distribution of the voters, these wasted votes can either be completely localised within a small portion of the electorate (less than one quota) or fractionally spread out amongst a larger share (who have portions of their votes transfer). Importantly, the more winners there are in a single constituency, the fewer votes that may be wasted under STV and therefore the more proportionate the outcome will be.

Related Topics:
Wasted vote - Proportionality

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The preferential ballot

Voters in a Single Transferable Vote election cast a preferential ballot that is a ranked, ordinal listing of their preferred candidates. Voters in STV elections have a significant incentive to list their preferences honestly, as doing so improves the likelihood of the voter attaining representation amongst the winning candidates (see tactical voting, below).

Related Topics:
Preferential ballot - Ordinal

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Many STV systems allow voters to give a partial list of preferences by only ranking a subset of the candidates, however this leads to the possibility of exhausted votes, where a vote, or portion of a vote, is unable to be transferred because there are no more candidates indicated on the exhausted ballot. To prevent exhausted ballots, some STV systems instead require voters to give a complete ordering of all the candidates in an election. However, when there is a large set of candidates this requirement may prove burdensome and can lead to voters ranking their final choices arbitrarily when they lack strong opinions ("Donkey voting"). To facilitate a complete ballot, some STV systems may provide the voter with the option of using group voting tickets rather than having to completely identify individual preferences.

Related Topics:
Donkey voting - Group voting ticket

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Counting the ballots

The quota (sometimes called the threshold) is the number of votes a candidate must receive to be elected. Votes are assumed to go to the top preference first, and are then transferred from eliminated candidates and the surpluses of winners until enough candidates meet the quota to fill the number of seats. To avoid unnecessary counting, candidates may instead be eliminated until the number of seats left to fill is the number of remaining candidates. This approach becomes necessary if ballots are allowed to be exhausted, as it then becomes possible for an insufficient number of candidates to reach the quota if the exhausted votes are numerous enough to fulfil a quota instead.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

STV systems differ in how they transfer votes as well as the exact size of the quota used for determining winners. The Droop quota, the most common, minimizes the size of the quota while still maintaining the condition that no more candidates can reach a quota than there are seats to be filled. While this still leaves nearly a quota's worth of votes unallocated (wasted), transferring these votes would not alter the eventual outcome. For example, Meek's method, the method of transferring votes adopted in the New Zealand STV system, utilizes a computer to evenly transfer portions of excess votes from winning candidates until they barely satisfy the quota, thereby taking into account transfers to already elected candidates. Meek's method also dynamically adjusts the quota during the counting process of the election, lowering it slightly to take account newly exhausted votes. In Meek's method, initially different ballots that express the same preferences after particular candidates are eliminated are weighted exactly the same - there is no penalty for ballots arriving at a candidate in an earlier round than others.{{ref|Hill}}

Related Topics:
Droop quota - Meek's method

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An example

Suppose a food election is conducted to determine what to serve at a party. There are five candidates, three of which will be chosen: oranges, tangerines, chocolate, strawberries, and candy. The 20 guests at the party have the preferences marked on their ballots in the table at the right, with each ballot being represented by a colored x. Note that in this example it is not needed for some of the voters to indicate a complete preference list, however in a larger election with more candidates the value of ranking additional preferences to the voter increases.

Related Topics:
Orange - Tangerine - Chocolate - Strawberries - Candy

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Note that if the quota were exactly 1 vote less, it would become possible for 4 candidates instead of 3 to fulfill it.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In this sample election, the number of wasted votes is 4: the three unsuccessful votes for candy in the final round that did not elect a candidate, plus one less than the difference between strawberry and candy's votes in the final round (5 and 3, respectively). This is 4/20, or 20% of all the votes cast.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~