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

[Ross Hyman]

I think this example shows by-election failure for most STV methods
(including, sadly, my own).
35 C>A>D>B
34 C>B>D>A
31 D>C>A>B
2 winners Droop quota 33 1/3.
C and D win.
exclude C.
A and B must win. If you force D to be a winner Droop proportionality
is violated.

Is there an STV-like method that initially elects C and A?

On Tue, Apr 21, 2026 at 12:25 PM Ross Hyman <rossahyman at gmail.com> wrote:
>
> 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