Editing Single transferable vote (section)

=== 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 (of the strawberry/chocolate variety), 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 vote{{snd}}they each mark their first preference and are also allowed to cast two back-up preferences to be used only if their first-preference food cannot be selected or to direct a transfer 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.

When the ballots are counted, it is found that the ballots are marked in seven distinct combinations, as shown in the table below:

{| class="wikitable"
|-
! 1st preference
| [[File:Emojione 1F34A.svg|50px|Orange|alt=Oranges]]
| [[File:Emojione 1F350.svg|50px|Pear|alt=Pears]]
| [[File:Emojione 1F353.svg|50px|Strawberry]]
| [[File:Emojione 1F370.svg|50x50px|Strawberry Chocolate Cake]]
| [[File:Emojione 1F36B.svg|50px|Chocolate]]
|[[File:Emojione 1F354.svg|50px|Hamburger]]
|[[File:Emojione 1F357.svg|50x50px|Chicken]]
|-
! 2nd preference
| [[File:Emojione 1F350.svg|50px|Pear|alt=Pears]]
| [[File:Emojione 1F353.svg|50px|Strawberry]]
| [[File:Emojione 1F34A.svg|50px|Orange|alt=Oranges]]
| [[File:Emojione 1F36B.svg|50px|Chocolate]]
| [[File:Emojione 1F370.svg|50x50px|Strawberry Chocolate Cake]]
|[[File:Emojione 1F357.svg|50x50px|Chicken]]
| [[File:Emojione 1F36B.svg|50px|Chocolate]]
|-
!3rd preference
|
| [[File:Emojione 1F370.svg|50x50px|Strawberry Chocolate Cake]]
|[[File:Emojione 1F350.svg|50px|Pear|alt=Pears]]
|
|[[File:Emojione 1F354.svg|50px|Hamburger]]
|
|[[File:Emojione 1F354.svg|50px|Hamburger]]
|-
!# of ballots
! 3
! 8
! 1
! 3
! 1
! 4
! 3
|}
The table is read as columns: the left-most column shows that there were three ballots with Orange as the first choice and Pear as second, while the right-most column shows there were three ballots with Chicken as first choice, Chocolate as second, and Hamburger as third.

The election step-by-step:
{| class="wikitable" style="text-align: center;"
! rowspan="2" |Step
! colspan="7" |Votes for each option
|-
! [[File:Emojione 1F34A.svg|50px|Orange|alt=Oranges]]
! [[File:Emojione 1F350.svg|50px|Pear|alt=Pears]]
! [[File:Emojione 1F353.svg|50px|Strawberry]]
! [[File:Emojione 1F370.svg|50x50px|Strawberry]]
! [[File:Emojione 1F36B.svg|50px|Chocolate]]
![[File:Emojione 1F354.svg|50px|Hamburger]]
![[File:Emojione 1F357.svg|50x50px|Hamburger]]
|-
! Setting the quota
| colspan="7" | The quota is 6 ([[Droop quota]])
|-
! Step 1
| 3
| 8
ELECTED

(2 surplus vote)
| 1
| 3
| 1
|4
|3
|-
!Step 2
|3
|ELECTED
| {{nowrap|1 + 2 {{=}} 3}}
|3
|1
|4
|3
|-
!Step 3
|3
|ELECTED
|3
| {{nowrap|3 + 1 {{=}} 4}}
|''eliminated''
|4
|3
|-
! Step 4
| {{nowrap|3 + 1 {{=}} 4}}
|ELECTED
| ''eliminated''
| {{nowrap|4 + 2 {{=}} 6}}
ELECTED

(0 surplus votes)
|''eliminated''
|4
|3
|-
! Step 5
| 4
|ELECTED
|''eliminated''
| ELECTED
|''eliminated''
| {{nowrap|4 + 3 {{=}} 7}}
ELECTED

(1 surplus vote)
|''eliminated''
|-
!Result
|
|ELECTED
|
|ELECTED
|
|ELECTED
|
|}

[[File:Single Transferrable Vote example.png|thumb|A [[Sankey diagram|Sankey chart]] illustrating the vote process. Not shown is the one-vote transfer from Strawberry to Oranges in Step 4.]]

'''Setting the quota:''' The [[Droop quota]] formula is used to produce the quota (the number of votes required to be automatically declared elected) = floor(valid votes / (seats to fill + 1)) + 1 = floor(23 / (3 + 1)) + 1 = floor(5.75) + 1 = 5 + 1 = 6

'''Step 1:''' First-preference votes are counted. Pears reaches the quota with 8 votes and is therefore elected on the first count, with 2 surplus votes. 

'''Step 2:''' All of the voters who gave first preference to Pears preferred Strawberry next, so the surplus votes are awarded to Strawberry.

No other option has reached the quota, and there are still two to elect with six options in the race, so elimination of lower-scoring options starts.

'''Step 3:''' Chocolate has the fewest votes and is eliminated. According to their only voter's next preference, this vote is transferred to Cake. No option has reached the quota, and there are still two to elect with five in the race, so elimination of options will continue next round.

'''Step 4:''' Of the remaining options, Oranges, Strawberry and Chicken now are tied for the fewest votes. Strawberry had the fewest first preference votes so is eliminated. In accordance with the next preference marked on the vote cast by the voter who voted Strawberry as first preference, that vote is transferred to Oranges. In accordance with the next preference marked on the two votes cast by the Pear–Strawberry–Cake voters (which had been transferred to Strawberry in step 2), the two votes are transferred to Cake. (The Cake preference had been "piggy-backed" along with the transfer to Strawberry.) Cake reaches the quota and is elected.

Cake has no surplus votes, no other option has reached the quota, and there is still one choice to select with three in the race, so the vote count proceeds, with the elimination of the least popular candidate.

'''Step 5:''' Chicken has the fewest votes and is eliminated. The Chicken voters' next preference is Chocolate but Chocolate has already been eliminated. The next usable preference is Hamburgers, so the three votes are transferred to Hamburgers.

Hamburgers is elected with 7 votes in total. Hamburgers now has a surplus vote, but this does not matter since the election is over. There are no more foods needing to be chosen{{Snd}}three have been chosen.

'''Result:''' 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{{Snd}}19 votes were used to elect the successful candidates. (Only the votes for Oranges at the end were not used to select a food. The Orange voters have satisfaction of seeing their second choice – Pears – selected, even if their votes were not used to select any food.)

As well, 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 front runners 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 front runners and sometimes none at all.<ref>{{Cite book |title=A Report on Alberta Elections |publisher=Alberta Legislature |year=1982 |pages=38–81}}</ref>

==== 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]] (SNTV), [[first-past-the-post]] (FPTP) in three districts, first-past-the-post at-large [[Group voting ticket|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 seen 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 win{{snd}}Oranges (or Chicken or Cake), 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 to bias the election toward a particular result could occur). It might have been Strawberry cake, Pears and Hamburgers, but also the foods chosen might have been Pears in two groups (districts) 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.

Using FPTP, it could happen that under any three-district single-winner system, none of the groups elect Pears, if the 7 votes for it are split and in each "district" there is another food that beats it (e.g. Oranges, Hamburgers and Chicken).

Similar problems arise to a lesser degree if all districts use a majority system instead of plurality (for instance, [[Two-round system|two-round]] or [[instant-runoff]] voting) 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 (first-past-the-post but without "districts"), it is likely that Pears, the choice of less 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 (as in the [[two-round system]]), the bare majority that prefers some other kind of fruit (Oranges, Pears, Strawberries) would have dominated all other choices.

Giving electors a {{em|single}} 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 there can be 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 [[Independence of clones criterion|clone candidates]]. For example, the seven 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 7 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 [[tactical voting|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.