A vote under STV may be used to elect the voter's first preference. Or it may be used to elect someone other than the voter's first preference (but still a candidate the voter prefers over others). Or it may not be used at all to elect anyone.
In STV elections, about 80 percent of the votes or more are used to elect someone. This is much larger portion than under First Past The Post where as few as 18 percent are sometimes used to elect the member. (See below for more info on this.)
Here are the possible outcomes of a vote under STV:
(I will use the whole vote system for simplicity sake. Even so, it is complicated. Don't know how to make it simple.)
A. first preference is marked for a candidate who is elected, elected either on the first count or later. The vote is considered as being used to elect the candidate and is left with the candidate. (those unable to be transferred are left with the successful candidate).
B. first preference is marked for a candidate who is elected, elected either on the first count or later. The vote is considered as being part of the surplus and is transferred to the next usable marked preference. The receiving candidate may be elected, in which case the vote either stays with that candidate or is transferred on (perhaps many times) to be used in the end to help elect another successful candidate (not the voter's first preference but someone the voter prefers over others).
C. first preference is marked for a candidate who is elected, elected either on the first count or later and is subsequently transferred but never is used to elect anyone. The vote is considered as being part of the surplus of the elected candidate and is transferred to the next usable marked preference. Perhaps that candidate is neither eliminated nor elected, so the vote is not transferred any more and is not used to elect anyone. The vote is counted among the votes not used to elect anyone. Or perhaps the candidate is eliminated, the vote (in these cases) are transferred to the next usable preference (and possibly to others as per back-up preferences in succession) until either being exhausted or at the end being cast for a candidate who is neither eliminated nor elected. These votes are counted among the votes not used to elect anyone.
D. first preference is marked for a candidate who is eventually eliminated. The vote is transferred to next usable preference and in some cases transferred again and again. The vote eventually is used to elect someone and is left with the successful candidate. (not the voter's first preference but someone the voter prefers over others)
E. first preference is marked for a candidate who is eventually eliminated. The vote is transferred to the next usable preference and in some cases transferred again and again and eventually rests with someone who is neither elected nor eliminated or on one of the transfers it is found to be exhausted and put in the exhausted pile. So it is not used to elect anyone. The vote is counted among the votes not used to elect anyone.
F. first preference is marked for a candidate who is eliminated and this elimination thins the field of candidates to just the number of remaining open seats. The votes are not transferred to next usable preference so are not used to elect anyone. The vote is counted among the votes not used to elect anyone. This vote was never transferred (if even the voter bothered to mark back-up preferences).
G. first preference is marked for a candidate who is neither eliminated nor elected. Vote is not transferred and is counted among the votes not used to elect anyone.
Not all votes are used to elect anyone but most are.
A votes are used to elect the voter's first preference and stay with that candidate
B votes are used to elect a member - not to elect the voter's first preference but to elect someone the voter prefers over others. (As well the voter saw his first choice elected although his or her vote was not used to elect that person.)
C votes are not used to elect anyone. (The voter did see his first choice elected although his or her vote was not used to elect that person.) (at end the vote is exhausted or left with a candidate who was neither elected nor eliminated)
D votes are used to elect a member - not to elect the voter's first preference but to elect someone the voter prefers over others. The vote stays with that candidate
E votes are not used to elect anyone.
F votes are not used to elect anyone.
G votes are not used to elect anyone.
So that is how some votes (A) are used to elect the voter's first preference. (The voter may see several of his later preferences elected as well - we don't know because the later preferences marked on the ballot are never looked at.)
Others (B and D) are used to elect someone the voter prefers over others but not the voter's first preference. In the case of B votes the voter saw his first choice elected although his or her vote was not used to elect that person. In the case of both B and D, the voter may see several of his preferences elected although the vote in the end is used just to elect one.
Some votes (some of C and E) are declared exhausted;
Some votes (some of C, some of E, all of F, and all of G) are neither exhausted nor used to elect anyone.
Percentages of each type of vote
In historic Canadian elections, speaking generally
A votes made up 33 percent of votes cast
B and D votes make up about half (50 percent) of votes cast
15 percent are exhausted (some of C votes and some of E votes)
5 percent or less are F -- votes that are neither exhausted nor used to elect anyone (they all belong to the last eliminated candidate when those votes are not transferred - he or she was popular enough to hang on to the end but was the least popular among the candidates still in the running at the end. (Possibly more than a quarter of quota but less than half?)
G votes were non-existent in Canadian STV elections. (see below)
A, B and D are used to elect someone. together comprising something like 80 percent of the votes.
G votes - votes for candidates who were neither elected nor eliminated
In Canada STV elections, all candidates were either elected or eliminated or defeated. Some elections saw a candidate declared defeated after the last numbered count. This was the least-popular candidate when the field of candidates thinned down to the number of remaining open seats. He or she was declared defeated after the last count so was not "eliminated", just declared defeated. By the time the field of candidates thinned down to that level, still, not all the seats were filled by candidates achieving quota. This was due to the number of exhausted votes being such that in the end it was impossible for all the seats to be filled by candidates with quota. So eliminations continued until the field of candidates was thinned to the number of remaining open seats, the least popular candidate was declared defeated, and the seats were filled by candidates with less than quota.
You can tell this because in most Canadian STV elections, one or two or three candidates were elected with partial quotas. This only happens when the field of candidates is thinned to the number of remaining open seats, and this means the votes of the last defeated candidates are not transferred. (Although in some computer STV elections that are being conducted outside Canada today, the votes are transferred but there is no reason for this transfer -- the seats are already filled.)
For the same reason, the C and E votes that are not exhausted but are not used to elect anyone do not exist in historic Canadian elections.
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Percentage of Effective Votes
The percentage of votes used to elect a candidate (or member if you prefer), whether first preference or someone else preferred by voter, is about 80 percent or more, with only a small percentage not being used to elect someone.
The source for this figure is any STV election result. A total of the votes used to elect a member are about that percentage of the valid votes. It can be found on page 145 of Hoag and Hallett, Proportional Representation (1926) as well:
Cleveland City council 1923 81 percent
"Effective Vote for Council" ("the number of ballots which helped elect councilmen")
Transfer of fractional votes
The use of transfers of fractional votes under the Gregory system used in some systems (such as in Australia and some Local Authority elections in Scotland) obscures that the basis of STV is single voting. Each person has just one vote.
Fractional votes are used only for votes transferred when a candidate is elected.
So to cover STV systems that use fractional vote transfers as well as systems that use whole vote transfers, I think it is safe to say :
some votes are used to elect the voters' first preference; some are not used to elect the voter's first preference but are used to elect someone the voter prefers over others; some are not used to elect anyone at all.
In some STV systems (such as Gregory systems), the vote may be broken into fractions. Under such systems, parts of a vote or all of it is used to elect one or more members, or only part of it is used to elect someone and the rest not used to elect anyone. Other votes are not broken into fractions -- they are either not used to elect anyone at all or are so used but are not transferred thereafter.
The percentage of votes cast in an STV election that are used to elect someone varies but experts and STV election results put the figure at about 80 percent or more. This compares well to First-past-the-post elections where as few as 18 percent are sometimes enough to elect the successful candidate, with all others not being used to elect a member.
sources
Hoag and Hallett, Proportional Representation (1926), p. 145
https://electoral.gov.mt/ElectionResults/General
https://www.toronto.ca/wp-content/uploads/2017/08/9021-election-2014-councillor-poll-by-poll-results.pdf
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A votes stay with first preference
B votes result from idea that an elected candidate should retain only the quota, thus allowing the surplus to be transferred to allow it to assist in the election of someone else. This ensures that each member is elected by same number of votes (except for those elected at the end)
B votes are transferred to another candidate of the same party sometimes or the transfer may cross party lines. When the last candidate of a party is elected, the surplus then goes to to possibly help someone of another party to be elected. That person is someone preferred by the voter who cast that ballot.
B votes show that someone not initially popular may accumulate vote transfer either from surplus votes of elected candidates or vote transfers form eliminated candidate described below) and their vote tally may surpass some the vote tally of someone else initially more popular. Votes that are transferred due to the use of back-up preferences are counted just as fully as first preferences (except when votes are transferred in fraction form (as in Gregory ) but then too the vote fractions is valued just as much as that fraction is.)
The candidate with more votes in the first count is not guaranteed to win in the end. For one thing, that candidate if not declared elected in the first count does not have quota. And if a initially lower ranking candidate surpasses his vote tally, then that means that that candidate is the more popular choice. And if only one of the two is to be elected it should be the most popular one, irrespective of first count popularity order.
A candidates are those elected on the 1st Count.
B candidates are those elected later by combination of some first preference votes and some votes marked with back-up preferences (B votes).
C candidates received C votes. These candidates are not elected but the voter has seen his or her first preference elected even if that vote was not used to elect the person.
D candidates are those elected later by combination of some first preference votes and some votes marked with back-up preferences (D votes).
E candidates never achieve quota and are neither eliminated nor elected or are declared exhausted.
F candidates never achieve quota and are eliminated at the end.
G candidates never achieve quota and are neither eliminated nor exhausted. They possess G votes plus any votes transferred to them from other candidates.
The H candidate is eliminated in the first elimination. He or she has only the votes that were cast for him or her as first preferences plus any votes transferred to him or her through surplus votes of candidates elected in the first count or any counts held to transfer surplus votes.
I candidates are elected through vote transfer from A candidates. (This includes some B candidates)
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Stage by stage
1st stage A candidates declared elected
2nd stage and so on transfer of surplus vote of A candidate, most popular first.
some go to B candidates who are elected with them and others;
some to C who are not elected;
some to D who are elected;
some to E who are not elected
if I candidates exist, they are declared elected and their surplus is transferred.
The H candidate is eliminated in the first elimination. (votes are transferred as D votes or C votes)
more candidates are eliminated (votes are transferred as D votes or C votes)
Finally all seats are filled through elimination and first count/first preference votes (A votes), those remaining are G candidates,
or
F candidate is eventually declared defeated, thinning the field of candidates to the number of remaining open seats. (There are no G candidates - all candidates have been either eliminated or elected or declared defeated.)
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"Used up but satisfied" votes -- A sub-category of Exhausted Votes
not identified as separate category in the usual STV transfers.
These are votes that are marked for candidate(s) already elected and with no usable back-up preference when the vote is up for transfer.
(Usually these are lumped in with the votes that are exhausted and have none of the marked preference being elected.)
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How do you count fractional votes?
Due to fractional vote transfers used in Gregory systems, a vote may be split into several fractions.
One system description explained the go-around the system uses to establish Effective Votes, when each successful candidate has a diverse mixture of fractional votes.
"In principle, we would calculate the Legislative Power Share scores on a ballot-by-ballot basis and include the effect of fractional ballot allocations.
Unfortunately, however, ballot-level data is not publicly available. We have therefore introduced a simplification in which we consider the total number of ballot-equivalents received by elected representatives.
In the counting process, most candidates accumulate a total number of ballots equal to the quota required to be elected, with any surplus ballot fractions being transferred to other candidates. In the final rounds of the count, the final candidate to be elected has typically received less than a full quota’s worth of votes, and other candidates may have received slightly more (if surplus transfers are not required to determine the final outcome, they are not carried out).
A given voter may have their ballot allocated in part to more than one candidate, but since we cannot track this fractionation process, we treat each ballot-equivalent that an elected candidate receives as representing one distinct voter."
from Norway Electoral authority -- STV (Ireland) :: Election Modelling (election-modelling.ca) ====================================
No easy way to cheat -- Strategies used under STV to maximize seats
Two different strategies are sometimes employed to try to maximize seats. Curiously, they are complete opposites, although having the same goal.
One strategy is to have first preferences as equally spread as possible. This works if a party is concerned about having as many candidates as possible survive to the end to scoop up transfers from other parties.;
The other strategy is to have one big winner in the first count with votes then "cascading" down to other party candidates. This works if voters mark back-up preference along party lines.
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