[EM] STV and single constraints, like gender quotas

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Hi Kristofer,
> 
> I don't consider Schulze STV, only standard STV (IRV-based, fractional
> static Droop quotas, not meek),
> since it is the only method, which is simple to explain to
> non-enthusiasts and widely used and have tested and widely used
> software support for vote counting.
> 
> I guess, that by the "naive approach" you mean: "elect seats normally,
> if during the vote-count the, same number of seats remain must belong
> to one quota group in order not to break the quota (i.e. if. all
> remaining seats must belong to one quota group), elect only candidates
> from this quota group.
> Do you also to the "naive approach" count "guarding" candidates from
> elimination, if it could mean not filling the quotas?

Yes. These are the Church of England rules mentioned in your first link. 
"If you need max 5 women, and 5 women have been elected, eliminate all 
remaining men; if you need min 5 women and only 5 women are left, 
protect them from elimination."

> I guess a combinatorial method is CPO-STV and Schulze-STV?

A combinatorial method is any method that considers all possible ways to 
assign candidates to seats, and then determines the best assembly 
according to some rule. CPO-STV and Schulze STV would be combinatorial 
methods, as would (exhaustive) PAV and birational voting.

> I consider only single constraints (i.e. no combination of women and
> skin color etc.).
> I didn't understand your proposal how "you could make ordinary STV
> combinatorial".

Okay, if you only consider single constraints, the Church rules should work.

As for making ordinary STV combinatorial, this is just trying to attach 
a metric to STV. Ordinary STV could be considered to elect the best 
assembly according to some measure involving the number of last-place 
votes for the candidates eliminated in each round. If that's the case, 
it should be possible to force STV to eliminate candidates in a certain 
order and then measure how "good" the resulting assembly is in 
comparison to the best possible. Then you could pick the one that is 
closest to best while still giving an assembly that passes the constraints.

For instance, say that ordinary STV for 2 seats goes like this:
A is elected
B is eliminated (first pref votes: C: 40, D: 35, B: 30).
C is elected
all done. This gets a score of 0, because the person with least last 
place votes was eliminated in the second round.

Then say we force D to be eliminated in the second round. Then we'd get:
A is elected
D is eliminated (fpv: C: 40, D: 35, B: 30). Penalty is 35-30 = 5.
B is elected (say).
all done. Then this has a penalty of 5 because STV "would have" 
eliminated B (at 30 first place votes) but you forced it to eliminate D 
(at 35) instead.

The problem is that, if you increase the number of seats, "eliminate D 
then eliminate B" is not the same thing as "eliminate B then eliminate 
D". To be fair, you'd only have to count the order which gives the least 
penalty, and it's not obvious to me how that would be done.

Besides, the method is extremely complex.