[EM] a solution to the by-election problem?

[Ross Hyman]

Perhaps I wrong about this.  Elect M winners using a Droop
proportional STV method. Exclude one of the winners from all ballots
and rerun the election for M winners, protecting the M-1 previous
winners from exclusion. Can someone present a proof that it will
always be the case that the new M winners (which must include the
previous M-1 winners) satisfy Droop proportionality? Or can someone
present a counter-example?

On Tue, Apr 21, 2026 at 5:21 AM Kristofer Munsterhjelm
<km-elmet at munsterhjelm.no> wrote:
>
> On 2026-04-20 23:39, Ross Hyman via Election-Methods wrote:
> > Hi all,
> >
> > The by-election problem is the following:
> > Starting with a Droop compliant solution for the M-winner problem,
> > exclude one of the M winners. Now determine a new set of M-winners
> > that includes the M-1 remaining previous winners and is also Droop
> > compliant. There is no STV method that does this. Either you preserve
> > Droop compliance but not all the M-1 previous winners are reelected,
> > or you protect the M-1 previous winners from exclusion and the new Mth
> > winner is not guaranteed to be Droop compliant.
>
> Don't combinatorial methods lke Schulze STV or CPO-STV do this?
>
> Do the Condorcet election with every superset of the (M-1) winners that
> have already been elected. Pick the winner according to the pairwise method.
>
> Or can they still work themself into a corner they can't get out of?
>
> -km