[EM] STV - the transferrable part is OK (fair), the sequential round elimination is not

[Raph Frank]

On Tue, Nov 3, 2009 at 7:41 AM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> Raph Frank wrote:
>> If there are 5 seats and you have 20%+ of the votes, you are
>> guaranteed to get 1 seat under both d'Hondt and Droop.

There is a typo there, I meant 4 seats and 20%+ (I replied in a different post).

> How about Sainte-Lague/Webster's? Since it's a divisor method, it would
> (seldomly) violate quota, and so a ballot-based version of it couldn't meet
> the DPC. Yet, I would say that such a version would (absent other flaws) be
> proportional - I just don't know how to actually construct it.

That might be possible by reducing the quota.  However, doing that
could result in to many candidates winning a seat.

If there are 4 seats, then a party is entitled to get 1 seat if they
get between 0.5 and 1.5 "seat's worth of votes".

In a 2 party situation, where 1 party gets 12.5%+ of the vote, the
smaller party will still get 1 seat, even though it is only much lower
than the Droop quota.

This is why most jurisdictions don't use the standard version.

Instead of dividing by

1,3,5,7,9,...

they divide by
1.4,3,5,7,9,...

The effect is that it is harder for parties to get their first seat.
Parties with 2 or more seats are no affected.

PR-STV is inherently made up of single candidate parties, so this
defect is much worse.

St. Lague divisors can also be specified as
0.5, 1.5, 2.5, 3.5, 4.5, ....

This gives a better comparison to d'Hondt.

Using d'Hondt for the first seat and St. Lague for the rest gives
1, 1.5, 2.5, 3.5, 4.5, ....

This is a little more severe of a penalty that the standard
modification.  However, it would reduce the "tiny party" exploit.

Applying that to PR-STV could be something like

-> candidates must designate what party they are members of

Initially, the Droop quota is used as Quota_single, but it might take
a bit of tweaking to find one that gives the right number of seats, in
any given election (like Webster's method).

When a party has some members elected, the quota is reduced for all
other members of the party (but max 1 candidate may be elected at a
time).

No elected party members

Quota = Quota_single

At least one party member elected

Quota = Quota_single*(0.5 - (Quotas held by elected members - seats held))

Surpluses are only transferable if the candidate exceeds Quota_single

Thus if a party had won 2 seats, and both had achieved the full quota,
then the next party member would only need 0.5 quotas to get elected,
as the party would have 2.5 quotas at that point (and that would be
rounded upwards to 3).

It might even be possible to adjust this in order to remove the
requirement that candidates declare which party they are members of.

It is a lot of complexity in order to remove the large party bias.

Some of the other methods like CPO-STV and Schulze might achieve the same thing.

Also, if the districts are only 5 or so seats in size, then it doesn't
really help that much at all, as only large parties will get more than
1 seat anyway, though it could help medium parties get a 2nd seat.

> If the limitations of apportionment methods are true for party-neutral
> multiwinner methods as well, then it's impossible to have both population
> pair monotonicity (what we usually call "monotonicity") and to always obey
> quota.

Well, PR-STV doesn't meet the monotonicity criterion.

I am not sure if an alternative elimination ording could help there,
but probably not.