# Can this paradox happen in single transferable vote?

Suppose we conduct a single transferable vote election and everyone has given their ranked preference of candidates. If we use these votes to elect three candidates, we get candidates A, B, and C. If we use them to elect four candidates, we instead get A, B, D, and E. C has lost their seat simply by having an additional seat be contested.

Is this a possible scenario?

• This is a reasonable outcome if the surporters of D and E both hate C less then the other candidates. Also need a few surporters of A and/or B to not hate D and E. Aug 26, 2021 at 15:00

Yes. Consider the following (somewhat contrived) scenario.

There are 300 voters and 5 candidates. The election uses the formula (number of votes) / (seats to fill) to determine the quota. Votes are as follows:

BE - 100

CE - 25

CD - 15

DC - 35

EC - 25

(Where "XY - Z" means Z people voted X as their first choice and Y as their second choice)

With 3 seats to fill, the quota is 100. A and B both reach that with no excess votes at all. This leaves C, D, and E with 40, 35, and 25 first-choice votes respectively.

Next, the candidate with the smallest number of votes (E) is eliminated and their votes are transferred to their second choice C. This process continues and D is eliminated transferring all their votes to C. The result is that C now has 100 votes and meets the quota.

Now let's try again with 4 seats to fill. This time the quota is 75, A and B still hit this, but they now each have 25 excess votes which are transferred to D and E. Now we have C, D, and E with 40, 60, and 50 first-choice votes respectively. C is now the candidate with the fewest votes so they are eliminated, transferring their votes to D and E who are elected.

There are other formulae that can be used to calculate the quota, but similar situations can be set up for them.

• I have never seen a situation were you transfer vote of the winner after their victory. it juste does not make sense and only work in your example because they all vote for the same second choice and you don't have to choose were to transfer them Aug 23, 2021 at 13:07
• @Bougainville, there are multiple methods of surplus handling used in STV elections (random, Gregory, Meek, etc) but they more or less aim to achieve the same purpose. See Wikipedia's Counting single transferable votes§Surplus allocation, for some examples. It would seem weird to "never see a situation" where surplus handling is used unless you've also "never seen a situation" where STV is used in a major election, since both the Republic of Ireland and Australia do it. Aug 23, 2021 at 13:39
• @Bougainville: STV does that to, essentially, avoid "wasting" the votes of people who rank a popular candidate first. Otherwise, it would encourage people to vote for a less popular candidate first, meaning the election might be less reflective of popular sentiment. Aug 23, 2021 at 15:12