Editing Single transferable vote (section)

===Transfers of surplus votes===
Various methods are used in STV systems to transfer surplus votes held by elected candidates. The transfer of surplus votes of an elected candidate may be very simply done or may be done more intricately, depending on the circumstances and the choice of the government or election officials.

It can happen that a vote is set to be transferred but cannot be because it bears no subsequent preference for any remaining candidate. In transfers of surplus votes, any non-transferable votes are left with the elected candidate.

If the number of transferable votes is less than the surplus, the transfer of surplus votes can be performed just as it is done in the case of transfer of votes of eliminated candidates, the only difference being that non-transferable votes remain with the elected candidate. They do not go to the exhausted pile. Transfer of the transferable votes is done in these cases simply by reference to the next usable preference on the vote.

In cases where the number of transferable votes is more than the surplus, a more-involved method may be used to make the transfer proportional and to ensure that the quota left with the successful candidate is proportional as well. But election officials here have a choice of using simpler methods or more involved methods.

Votes to the number of the surplus can be drawn at random from the candidate's votes. Choosing the votes at random from the pile means that each transfer should be mixed and will likely closely resemble the composition of the entire pile. (This is the system used in [[Cambridge, Massachusetts]], city elections.) <ref>{{cite web | url=https://www.opavote.com/methods/cambridge-stv-rules | title=Cambridge STV Rules }}</ref>

In the STV systems used in the Republic of Ireland (except Senate elections) and Malta, the next preference is examined and then surplus votes are transferred as whole votes in proportion to the proportions of votes marked for each of the other candidates. This is called the "exact method".<ref>{{cite book |last1=Hoag |first1=Clarence Gilbert |first2=George Hervey |last2=Hallett |title=Proportional representation |location=New York |publisher=The Macmillan Company |date=1926}}</ref> Randomness may arise from the later preferences, if any, if they have to be used later. But if they do have to be used later, choosing the votes at random to compose each transfer means that the votes that make up each transfer should carry back-up preferences in approximately true proportion to the whole.

The basic formula for how to transfer surplus votes when there are more transferable votes than the surplus to be transferred is:

<math display="block">
\begin{align}
& \text{transferred votes given to the next preference} \\[6pt]
= {} & \left( \frac{\text{votes for next preference belonging to the original candidate}} {\text{total votes for the original candidate or total transferable votes}} \right) \times \text{surplus votes for original candidate}
\end{align}
</math>

This can produce fractional votes, which are handled differently under different [[Counting single transferable votes|counting methods]].

Transferring votes without considering later preferences may influence later transfers and such systems are sometimes thought of as being random. Alternatively, some jurisdictions use systems that break down the elected candidate's votes into many separate piles, separating the various combinations of marked preferences on the ballots, or do the same by transferring part of each vote at the transfer value rate. The vote is transferred in the form of the ballot paper, carrying its own back-up preferences with it for possible later use. This is the [[Gregory method]].

The Gregory method (also known as Newland–Britain or Senatorial rules) eliminates randomness by examining all the preferences marked on the last parcel of ballots received by the elected candidate. The later preferences dictate how later transfers, if any, will go. Votes are transferred as fractions of votes. Gregory is in use in Northern Ireland, the Republic of Ireland (Senate elections) and in some electoral systems used in Australia.

Variants exist under the names inclusive Gregory method (IGM) and the weighted inclusive Gregory method (WIGM).{{sfn|Hill|Wichmann|Woodall|1987}}<ref>{{Cite web |last=Gilmour |first=James |date=March 2021 |title=Review of some aspects the Single Transferable Voting system for local elections in Wales |url=https://www.researchgate.net/publication/350495590 |access-date=26 November 2022 |website=ResearchGate}}</ref> WIGM is used in the Scottish local government elections.{{Citation needed|date=January 2024}} Unlike the ordinary Gregory method, these systems look at secondary preferences on all the votes held by the elected candidate, not just the votes that make up the last parcel of votes received.<ref>{{Cite web| title=Making Every Vote Count – The Case for Electoral Reform in British Columbia | url=https://citizensassembly.arts.ubc.ca/resources/TechReport(full).pdf | archive-url=https://web.archive.org/web/20171115220437/http://citizensassembly.arts.ubc.ca:80/resources/TechReport(full).pdf | archive-date=15 November 2017}}</ref>

Both Gregory and earlier methods have the problem that, in some circumstances, they do not treat all votes equally. For this reason, [[Meek's method]], [[Warren's method]] and the [[Wright system]] were invented.

Meek, in 1969,{{sfn|Meek|1994a}} was the first to realize that computers make it possible to count votes in a way that is conceptually simpler and closer to the original concept of STV. One advantage of Meek's method is that the quota is adjusted at each stage of counting when the number of votes decreases because some become non-transferable.<!--Add some history of when Meek came along, please. Note he was attempting to eliminate the problem of tactical voting while still maintaining proportionality and such--> Meek also considered a variant of his system which allows for equal preferences to be expressed.{{sfn|Meek|1994b}} This has subsequently (since 1998) been used by the [[John Muir Trust]] for electing its trustees.<ref>{{cite web |title=Examples of STV elections |url=http://www.macs.hw.ac.uk/~denis/stv_elections |publisher=Heriot-Watt University}}</ref>