# [EM] Let's fill the vacancy with the runner-up:

Bjarke Dahl Ebert bjarke2003 at trebe.dk
Tue Nov 11 11:30:01 PST 2003

```Donald Davison wrote:

>If the voters wanted a candidate of the same party they would have selected
>someone of the same party as the runner-up.  If we don't want to rework the
>ballots from the original election then we should merely select the first
>runner-up as the person to fill the vacancy.  Doing this is acceptable
>because the first runner-up has more votes than any other unelected
>candidate and would most likely win the seat if the ballots were reworked.
>
>

But what exactly is a runner-up in STV?
When the (plain) STV algorithm terminates there are not enough votes
"remaining" to elect a single candidate, so any method to choose a
runner-up from the remaining votes is in any case doubtful, IMHO.
One definition could be "the one who would get a set if n+1 were to be
elected", but the problem is that "n+1 elected candidates" may not
always include the original "n elected candidates".
You write: "because the first runner-up has more votes than any other
unelected candidate". You seem to forget that voters have had their
ballots "reduced" when electing the now leaving candidate, L. So the
runner-up is probably not elected by the L-voters, but by all the
voters, collectively.

I think the runner-up must depend on which candidate is leaving. Compare
with the PR party list case. If a candidate from party A leaves, a new
candidate from A replaces him/her. So who comes in depends on who is
leaving.

I think the best method, if the replacement must be determined from the
original STV election result, is to eliminate the leaving candidate from
all ballots, then repeat the STV count with the constraint that the n-1
remaining seats must be kept (cannot be eliminated). It must be possible
to do this also with SSTV, CLE-STV, CPO-STV and any other STV method.

- Bjarke

```