Filling a vacated seat using STV
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a
vacated seat by recalculating the original vote while simply excluding the
candidate who took that vacated seat? Could a situation arise where this
recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
35: A > C > D
33 B > C
17 C > D
15 D > B
Two winners: A and B win.
Exclude A: C and D win.
On Wed, Apr 8, 2026 at 5:27 PM Luděk Belán via Election-Methods
election-methods@lists.electorama.com wrote:
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a vacated seat by recalculating the original vote while simply excluding the candidate who took that vacated seat? Could a situation arise where this recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
Election-Methods mailing list - see https://electorama.com/em for list info
Thank you, but in your example, with the Droop quota (specifically quota 34)
I also get candidate C as the new winner, yet the second winner comes out as
candidate D or B because they have the same number of votes. With the Hare
quota, the new winners are candidates C and B; thus candidate A would be
replaced by candidate C. And is it possible to find a counterexample for the
unrounded Hare quota?
Luděk Belán
---------- Původní e‑mail ----------
Od: Ross Hyman rossahyman@gmail.com
Komu: Luděk Belán LudekBelan@seznam.cz
Kopie: election-methods@electorama.com
Datum: 9. 4. 2026 0:59:36
Předmět: Re: [EM] Filling a vacated seat using STV
"35: A > C > D
33 B > C
17 C > D
15 D > B
Two winners: A and B win.
Exclude A: C and D win.
On Wed, Apr 8, 2026 at 5:27 PM Luděk Belán via Election-Methods
election-methods@lists.electorama.com wrote:
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a
vacated seat by recalculating the original vote while simply excluding the
candidate who took that vacated seat? Could a situation arise where this
recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
Election-Methods mailing list - see https://electorama.com/em for list
info
"
The Proportional Representation Society of Australia recommends vacancies
are filled by the "countback" procedure. References:
[1] https://www.prsa.org.au/countbac.htm
[2] https://represent.org.au/countback/
As a practical matter, though, it's not always straightforward to recover
the quota of votes that elected the vacating candidate at the original
election and then perform the countback. There are other methods that are
not as ideal, but they're usually easier to implement and probably
equivalent for most cases in practice:
- Rerun the election with the vacating candidate removed, as you
described, but declare the vacancy filled by the first candidate to reach
quota who was not elected in the original election. - Fill the vacancy with the next-highest vote getter from the original
election
We can all come up with examples where these methods are not ideal, but
might be practically acceptable, especially if the term of office isn't
particularly long.
Greg
On Wed, Apr 8, 2026 at 8:51 PM Luděk Belán via Election-Methods <
election-methods@lists.electorama.com> wrote:
Thank you, but in your example, with the Droop quota (specifically quota
34) I also get candidate C as the new winner, yet the second winner comes
out as candidate D or B because they have the same number of votes. With
the Hare quota, the new winners are candidates C and B; thus candidate A
would be replaced by candidate C. And is it possible to find a
counterexample for the unrounded Hare quota?
Luděk Belán
---------- Původní e‑mail ----------
Od: Ross Hyman rossahyman@gmail.com
Komu: Luděk Belán LudekBelan@seznam.cz
Kopie: election-methods@electorama.com
Datum: 9. 4. 2026 0:59:36
Předmět: Re: [EM] Filling a vacated seat using STV
35: A > C > D
33 B > C
17 C > D
15 D > B
Two winners: A and B win.
Exclude A: C and D win.
On Wed, Apr 8, 2026 at 5:27 PM Luděk Belán via Election-Methods
election-methods@lists.electorama.com wrote:
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a
vacated seat by recalculating the original vote while simply excluding the
candidate who took that vacated seat? Could a situation arise where this
recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
Election-Methods mailing list - see https://electorama.com/em for list
--
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Voter Choice Massachusetts
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p :: 617.835.9161
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:: Follow us on Facebook https://www.facebook.com/yeson2rcv and Twitter
https://twitter.com/yeson2rcv ::
I was using quota 33 1/3.
On Wed, Apr 8, 2026 at 7:43 PM Luděk Belán LudekBelan@seznam.cz wrote:
Thank you, but in your example, with the Droop quota (specifically quota 34) I also get candidate C as the new winner, yet the second winner comes out as candidate D or B because they have the same number of votes. With the Hare quota, the new winners are candidates C and B; thus candidate A would be replaced by candidate C. And is it possible to find a counterexample for the unrounded Hare quota?
Luděk Belán
---------- Původní e‑mail ----------
Od: Ross Hyman rossahyman@gmail.com
Komu: Luděk Belán LudekBelan@seznam.cz
Kopie: election-methods@electorama.com
Datum: 9. 4. 2026 0:59:36
Předmět: Re: [EM] Filling a vacated seat using STV
35: A > C > D
33 B > C
17 C > D
15 D > B
Two winners: A and B win.
Exclude A: C and D win.
On Wed, Apr 8, 2026 at 5:27 PM Luděk Belán via Election-Methods
election-methods@lists.electorama.com wrote:
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a vacated seat by recalculating the original vote while simply excluding the candidate who took that vacated seat? Could a situation arise where this recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
Election-Methods mailing list - see https://electorama.com/em for list info
This method is used in Malta where Parliamentary candidates are allowed to stand in more than one constituency but are allowed to be elected as a Member of Parliament for only one constituency. If a candidate is elected in, say, two constituencies, they stand down in one constituency, creating an immediate ‘casual vacancy’ which is then filled by ‘counting again’ the STV ballot papers passing over any preferences for the candidate who has ‘withdrawn’.
James Gilmour
Edinburgh, Scotland
From: Election-Methods [mailto:election-methods-bounces@lists.electorama.com] On Behalf Of Ludek Belán via Election-Methods
Sent: 08 April 2026 23:08
To: election-methods@electorama.com
Subject: [EM] Filling a vacated seat using STV
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a vacated seat by recalculating the original vote while simply excluding the candidate who took that vacated seat? Could a situation arise where this recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
--
This email has been checked for viruses by Avast antivirus software.
www.avast.com
Thank you all.
In the meantime I have found that the STV method with the Hare quota can,
when used to fill a vacancy by recalculating the original vote (omitting the
preferences for the replaced candidate), also eliminate one of the
originally elected candidates. Therefore I consider a suitable method for
filling vacancies to be STV with a prohibition on eliminating originally
elected candidates — that is, the weakest candidate to be eliminated should
be sought only among the candidates who were originally unelected.
Luděk Belán
Třebíč, Czech Republic
---------- Původní e‑mail ----------
Od: James Gilmour jamesgilmour@f2s.com
Komu: 'Ludek Belán' LudekBelan@seznam.cz, election-methods@electorama.com
Datum: 9. 4. 2026 13:51:00
Předmět: RE: [EM] Filling a vacated seat using STV
"
This method is used in Malta where Parliamentary candidates are allowed to
stand in more than one constituency but are allowed to be elected as a
Member of Parliament for only one constituency. If a candidate is elected
in, say, two constituencies, they stand down in one constituency, creating
an immediate ‘casual vacancy’ which is then filled by ‘counting again’ the
STV ballot papers passing over any preferences for the candidate who has ‘
withdrawn’.
James Gilmour
Edinburgh, Scotland
From: Election-Methods [mailto:election-methods-bounces@lists.electorama.
com] On Behalf Of Ludek Belán via Election-Methods
Sent: 08 April 2026 23:08
To: election-methods@electorama.com
Subject: [EM] Filling a vacated seat using STV
Hello everyone,
does anyone happen to know whether the STV method can be used to fill a
vacated seat by recalculating the original vote while simply excluding the
candidate who took that vacated seat? Could a situation arise where this
recalculation would cause someone else to lose their seat?
Thank you.
Kind regards
Luděk Belán
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