Single transferable vote


The single transferable vote or proportional-ranked choice voting, also known as PR-STV and "proportional representation by means of the single transferable vote", is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
STV is a family of multi-winner proportional representation electoral systems. The proportionality of its results and the proportion of votes actually used to elect someone are equivalent to those produced by proportional representation election systems based on lists. STV systems can be thought of as allowing solid coalitions to cast voter-determined lists of individual candidates in elections using the largest remainders method to elect the winning candidates, rather than list-based proportional systems where voters cast their ballot for lists of already grouped candidates. Surplus votes belonging to winning candidates may be thought of as remainder votes. Surplus votes may be transferred from a successful candidate to another candidate and then possibly used to elect that candidate.
Under STV, votes are transferred to a voter's subsequent preferences if necessary, and depending on how the voter marked their preferences, a vote may be transferred across party lines, to a candidate on a different party slate, if that is how the voter marked their preferences. This allows voters of parties with too few votes to win a seat for their own candidates to have an effect on which candidates of parties with more support are elected. Additionally, this means most voters' preferences contribute to the election of a candidate they supported rather than being wasted on candidates who were not elected or on candidates who received more votes than needed to achieve election.
Under STV, no one party or voting bloc can take all the seats in a district unless the number of seats in the district is very small or almost all the votes cast are cast for one party's candidates. This makes it different from other commonly used candidate-based systems. In winner-take-all or plurality systemssuch as first-past-the-post, instant-runoff voting, and block votingone party or voting bloc can take all seats in a district.
The key to STV's approximation of proportionality is that each voter effectively only casts a single vote in a district contest electing multiple winners, while the ranked ballots allow the results to achieve a high degree of proportionality with respect to partisan affiliation within the district, as well as representation by gender and other descriptive characteristics. The use of a quota means that, for the most part, each successful candidate is elected with the same number of votes. This equality produces fairness in the particular sense that a party taking twice as many votes as another party will generally take twice the number of seats compared to that other party.
Under STV, winners are elected in a multi-member constituency or at-large, also in a multiple-winner contest. Every substantial group within the district wins at least one seat: the more seats the district has, the smaller the size of the group needed to elect a member. In this way, STV provides approximately proportional representation overall, ensuring that substantial minority factions have some representation.
There are several STV variants. Two common distinguishing characteristics are whether or not ticket voting is allowed and the manner in which surplus votes are transferred. In Australia, lower house elections do not allow ticket voting ; some but not all state upper house systems do allow ticket voting. In Ireland and Malta, surplus votes are transferred as whole votes and neither allows ticket voting. In Hare–Clark, used in Tasmania and the Australian Capital Territory, there is no ticket voting and surplus votes are fractionally transferred based on the last parcel of votes received by winners in accordance with the Gregory method. Systems that use the Gregory method for surplus vote transfers are strictly non-random. Other distinguishing features include district magnitude, how to fill casual vacancies, and the number of preferences that the voter must mark.
Unlike party-list proportional representation, under STV voters vote for candidates rather than for parties. STV is also different from the single non-transferable vote election system, a semi-proportional system where candidates are not ranked and votes are not transferred.

Process

In a single transferable vote system, the voter ranks candidates in order of preference on their ballot. A vote is initially allocated to the voter's first preference.
A quota is calculated by a specified method, and candidates who accumulate that many votes are declared elected. In many STV systems, the quota is also used to determine surplus votes, the number of votes received by successful candidates over and above the quota. Surplus votes are transferred to candidates ranked lower in the voters' preferences, if possible, so they are not wasted by remaining with a candidate who does not need them.
If seats remain open after the first count, any surplus votes are transferred. This may generate the necessary winners. As well, least popular candidates may be eliminated as a way to generate winners.
The specific method of transferring votes varies in different systems. Transfer of any existing surplus votes is done before eliminations of candidates. This prevents a party from losing a candidate in the early stage who might be elected later through transfers. When surplus votes are transferred under some systems, some or all of the votes held by the winner are apportioned fractionally to the next marked preference on the ballot. In others, the transfers to the next available marked preference is done using whole votes.
When seats still remain to be filled and there are no surplus votes to transfer, the least popular candidate is eliminated. The eliminated candidate's votes are transferred to the next-preferred candidate rather than being discarded; if the next-preferred choice has already been eliminated or elected, the procedure is iterated to lower-ranked candidates.
Counting, eliminations, and vote transfers continue until enough candidates are declared elected or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected.

Example for a non-partisan election

Suppose an election is conducted to determine what three foods to serve at a party. There are seven choices: Oranges, Pears, Strawberries, Cake, Chocolate, Hamburgers and Chicken. Only three of these may be served to the 23 guests. STV is chosen to make the decision, with the whole-vote method used to transfer surplus votes. The hope is that each guest will be served at least one food that they are happy with.
To select the three foods, each guest is given one votethey each mark their first preference and are also allowed to cast two alternate preferences to be used only if their first-preference food cannot be selected or to direct a transfer of their vote if the first-preference food is chosen with a surplus of votes. The 23 guests at the party mark their ballots: some mark first, second and third preferences; some mark only two preferences. The alternate preferences are used as needed in successive rounds of counting.
When the ballots are counted, it is found that the ballots are marked in seven distinct combinations, as shown in the table below:
1st preference
2nd preference
3rd preference
# of votes with combination3813143

The election round by round:
The winners are Pears, Cake, and Hamburgers.
Orange ends up being neither elected nor eliminated.
STV in this case produced a large number of effective votes: 19 votes were used to elect the successful candidates.
Also, there was general satisfaction with the choices selected. Nineteen voters saw either their first or second choice elected, although four of them did not actually have their vote used to achieve the result. Four saw their third choice elected. Fifteen voters saw their first preference chosen; eight of these 15 saw their first and third choices selected. Four others saw their second preference chosen, with one of them having their second and third choice selected.
Note that if Hamburger had received only one vote when Chicken was eliminated, it still would have won because the only other remaining candidate, Oranges, had fewer votes, so would have been declared defeated in the next round. This would have left Hamburger as the last remaining candidate to fill the last open seat, even if it did not have quota.
As in many STV elections, most of the candidates in winning position in the first round went on to be elected in the end. The leading frontrunners were Pears and Hamburgers, both of whom were elected. There was a three-way tie for third between Cake, Chicken and Oranges, Cake coming out on top in the end. Transfers seldom affect the election of more than one or two of the initial frontrunners and sometimes none at all.

Compared to other systems

This result differs from the one that would have occurred if the voting system used had been non-PR, such as single non-transferable vote, first-past-the-post in three districts, first-past-the-post at-large group ticket voting as used to elect members of the US electoral college, or a single-winner winner-take-all system in three districts.
Single non-transferable vote would have elected Pears and Hamburgers, and produced a three-way tie for third place with Oranges, Cake and Chicken tied. The tie would have been resolved by the flip of a coin or the choice of an election official. Possibly Oranges or Chicken would have been determined to be the winner among the three, even though Cake was seen in the vote count process to have more general support. Under SNTV, 15 voters would have seen their first preference winOranges, Pears and Hamburgers. Eight voters would have not seen their first-preference food served. The pro-Oranges voter, if Oranges was not chosen, may have been consoled by their second choice, Pears, being served, but the others would not be served any of the foods they like, except maybe the voter who likes Strawberry and the one who likes Chocolate whose third choice, Hamburgers, was a winner. At least three voters would not be served any of their favorites.
Under first-past-the-post, the guests would have been split into three groups with one food chosen by each group based on just the most popular food in each group. The result in this case would have been dependent on how the groups are formed. Gerrymandering of the groups could occur to bias the election toward a particular result. It might have been Strawberry cake, Pears and Hamburgers, but also the foods chosen might have been Pears in two groups and Hamburgers in the other. Or even just Pears alone might have won in each of the three "districts", in which case only 8 guests out of 23 would have seen their first choice served, a very unrepresentative outcome, given that three different foods could have been served.
Conversely, the use of FPTP under any three-district single-winner system could ensure that none of the groups elect Pears, if the 8 votes for it are split and, in each "district", there is another food that beats it.
Similar problems arise to a lesser degree if all districts use a majority system instead of plurality as at least in all districts the majority would have been quite happy, but that still leaves the minority unrepresented.
If the voters had been able to choose only one food to serve such as in the ticket voting system used in the US electoral college, it is likely that Pears, the choice of little more than a third of the 23 party-goers, would have won, meaning Pears would be the only food served at the party.
Even if they held two rounds of voting, the bare majority that prefers some other kind of fruit would have dominated all other choices.
Giving electors a transferable vote is very different from simply having more seats to fill and giving each voter more votes to cast. Plurality block voting is such a system. Under it, each voter is given as many votes as the number of winners. This system can produce very unrepresentative results. In the example above, if every voter voted for three options, the small majority of voters who chose a fruit could easily force all three outcomes to be fruit of some kind: an outcome that is unlikely to be more representative than simply choosing only one winner. In an extreme example, where no faction can command an absolute majority, the largest of the minority groups can force a one-outcome result by running clone candidates. For example, the eight supporters of Pears could arrange in advance to have three types of Pears included on the ballot, then vote for all three, and if no other option reaches more than seven votes, all three foods served would be a type of Pear. The only way this could be avoided would be for those who do not want Pears to vote tactically, by not voting for their preferred option but instead voting for whatever they consider to be the least bad outcome that is still likely to gain the required number of votes.