[EM] Multiwinner runoffs (Re: Proportional Representation Systems I'd Support)

Raph Frank raphfrk at gmail.com
Sat Mar 27 09:09:05 PDT 2010

On Sat, Mar 27, 2010 at 9:30 AM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> Raph Frank wrote:
>> This is less complex, but not as fair as transferring the surpluses.
> Your first method is more proportional than your second. If what you
> want is a majoritarian/centrist outcome, use the second.

They are both equally proportional, at least under strategy.

In any case, the idea was to ensure monotonicity in the first stage by
removing elimination steps.

It also has the equivalent to the majority rule.  If N candidates get
the Droop quota in the first round, then no 2nd round is required.

> In a runoff, to the extent possible, you'd want the
> two-round method to return the same result as an automated version of the
> one-round method if everybody voted equally: a top two runoff should return
> the same result as the contingent vote if everybody submitted the exact same
> ballots for the first and second round.
> However, if the outcome for q winners doesn't include the outcome for K
> winners, that is impossible.

Right.  However, my method did do that.  Effectively, it ran PR-STV as
normal until an elimination was required.

If everyone submitted the same ballot for the 2nd round, then the
candidates who hit the quota in the first round would be guaranteed to
hit the quota in the 2nd round.

What it doesn't do is guarantee that that, in a 5 seats race, the 6
candidates selected to make it to the 2nd round would contain the 5
PR-STV winners for the first round.

> Proportional orderings also have the Left-Right-Center problem. Just to
> repeat it: consider an electorate split between Left and Right, but both
> preferring Center to the other pole. A proportional ordering either picks
> Center for single-winner (as should be) but produces an unbalanced council
> for council size 2, or produces a balanced (Left, Right) council for size 1
> but fails to elect the centrist in the single-winner case.

Yeah.  This also applies to methods like sequential proportional
approval voting and reweighted score voting.

> An even nicer thing to have would be a proportional ordering based on
> Approval: then voters could pick acceptable candidates out of a large
> number, and later consider these more carefully. Once, I proposed using
> ordinary Approval for that purpose, but Benham (I think?) showed that that
> would not be cloneproof: a "rich party" could simply flood the initial
> selection with its candidates, and as long as the party got a plurality, all
> those candidates would be elected and so crowd out the others.


However, you could use sequential proportional approval voting.  Each
ballot is deweighted by

1/(k + number of elected candidates approved by voter)

k = 0.5 -> Sainte-lague - like
k = 1.0 -> d'Hondt - like

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