[EM] PR favoring racial minorities

[Raph Frank]

On Mon, Aug 25, 2008 at 8:10 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> That could work, since additional votes for A increase the weighting,
> meaning that a vote for A isn't wasted even if A wins.

Right, you basically lose your share of the votes that went to allow A to win.

> Let's look at that case, with two parties. Call them A and B. A wins 51% of
> every constituency, and that this amounts to 51 votes (thousand votes,
> whatever) out of 100. Then if there are as many top-up seats as there are
> ordinary seats, nearly all of the latter should go to B. Since there are two
> parties, by the reweighting above, the A voters would have strength
> (51-49)/51 = about 0.04. If there are 90 constituencies and thus 90 list
> seats, and all the A voters vote for A, nationally, as well, they'll have 51
> * 90 * 0.04 = 183.60 votes worth. Meanwhile, the B voters have 49 * 90 =
> 4410 votes worth. The total is 183.60+4410 = 4593.60, so A gets round(p *
> 183.60/4593.60) and B gets round(p * 4410/4593.60) with p chosen so that the
> sum is 90. This turns out to be p = 90, A gets 4 seats and B gets 86 seats.

That's fine.  In fact, if you had 50% local and 50% national seats,
then it can be made to work perfectly.

Just say that an independent must get at least 50% of the constituency
to be elected and if he does, each of his voters have their weights
reduced to

(VA-50%)/100% where VA is his percentage vote share

This gives perfect proportionality.

In effect, it 'costs' 50% of a constituency to win a seat, and the
independent has managed it and so gets a seat.  The candidate's
supporters 'spend' enough votes to elect the candidate and the rest go
to the national count.

IRV could even be used to make it a little fairer to possibly push a
candidate over the 50% mark.  (Exhausted ballots wouldn't affect the
quota, so 50% would be a true majority).  Any ballots which end up
with the independent would be de-weighted if he is elected.  This
would mean that voters would be advised not to rank independents that
they don't actually want to get elected.

> In total, A has 94 seats and B has 90. 94 out of 180 is 51.1% which isn't
> too bad, considering A had 51% support everywhere.
>
> So reweighting seems to work, at least in this case. If there are fewer
> top-up seats than constituency seats, the equation would have to be
> adjusted.

It works because there is enough seats left to counter balance the
original imbalance.

If there were 50 top-up and 100 local, then the A party would get 100
and the B party would be assigned all of the top-up seats.

Under some rules, the number of top-up seats can depend on the results
of the election.

One rule is that all parties must get at least 1 seat assigned.  An
independent on 50% of a district wouldn't get assigned any seats until
the number of national and local seats was equal.

Another option would be saying that if any independent gets elected,
the number of top-up seats must be equal to the number local seats.

A less severe version would be to activate the rule if more than x%
(say 5%) of the legislature are independents.  This would still cause
slight imbalances, but shouldn't be major.  It would also prevent a
major party using the decoy list strategy as if they did, it would
trigger the rule and thus cancel out the effect, as there would be
enough seats to completely compensate.

> Instead of a party point of view, how about an opinion point of view? The
> voters for independents also have opinions, and so their opinion should
> affect the national level (as it would explicitly if this was a national
> election).

However, the problem is that there is no way to combine them at the
national level.  It ends up with lots of candidates not having a
seat's worth of votes.

> As mentioned earlier, the voters that vote for an independent
> would probably vote for the party closest to the point of view of that
> independent if they have to vote for a party. As such, the shift in national
> influence is not an artifact, since the voters do have the corresponding
> opinion. With a good normalization system (reweighting or quota-based), the
> shift won't be very large if the independent actually got elected, but it'll
> exist -- ideally to the extent that there was a surplus.

The thing is that the surplus is the surplus above 1 seats worth of
votes, not surplus over the votes needed to win the constituency.

We are somewhat talking past each other here, as we are looking at it
differently, I think I have another way of expressing it.

My issues is that there are 2 types of candidates

- party candidates

If a party candidate wins a seat, they get 100% of the representation
for that constituency.  However, this is compensated by the fact that
they count as 1 seat won for the party.

This votes budget for that district is

Winner won a local seat
+ 1 local seat for the party

Winner counts as a party member
- 1 national seat for the party

All party votes added to party list totals as normal (1 person, 1 vote = fair)

By assigning the seat to the local winner, the winner's party loses a
seat at the national level, so it is neutral.

- independents

Winner won a seat
+1 seat for the independent

Candidate doesn't count as a member of any party
No effect on national vote

All party votes added to party list as normal (1 person, 1 vote)

Here, despite the winner winning a seat, all of his supporters still
get full effect at the national level.

Even if their votes were not eligible for the national count, it still
isn't fair as it hasn't cancelled a full seats worth of votes.

> I guess I should be more precise. What I meant was that the voters do not
> vote strictly according to any party's wishes on the constituency ballot.
> They do, however, vote for various (different) parties on the list ballot.
> If no candidate has a 2/3 majority in the constituency, that constituency
> still has to elect a candidate. Okay, that's fair enough. But now you can't
> use quota-based adjustment, since neither of the candidates met the quota,
> so it seems your adjustment must be based on the votes cast, or on relative
> support. In ordinary STV, you could just eliminate all the candidates, but
> the district constraint prevents that.

If no independent meets the threshold, give it to the party based
candidate who gets the most votes.  The only condition is that the
candidate's party must have enough spare national seats.

The process could be

Local count
1) Count all local votes
2) Assign each district to the, independent who exceeded the threshold
or party candidate, with the most votes
3) Reduce weight of ballots cast by voters for winning independents
4) Announce votes for each party (including any weighting) and votes
for each candidate
(constituencies are undefined if won by an independent who didn't hit quota)

National count
1) Work out how many seats each party is entitled to
2) Find candidate who stood in an undefined constituency, who has the
most votes and who's party is entitled to more seats.
3) Declare that candidate a winner and repeat until there are no such
candidates.
4) Declare any remaining undefined constituencies using some other
rule ... this shouldn't happen if all parties run candidates in every
constituency
5) Assign top-up seats in accordance with party lists so that each
party has the correct number of seats.

In that case, it doesn't matter which one of them wins the seat as
assigning them a seat is compensated by a seat at the national level,
so proportionality is maintained.

>> Anyway, I guess my concern is shown by the decoy list strategy.
>> Fundamentally, MMP allows an independent to get a seat while not
>> having enough votes to be entitled to that seat.  This leads to
>> potential abuse or just unfairness.
>
> Is that, in your opinion, a problem inherent to single-winner methods, or
> just to MMP as it's usually employed?

That's a good point.  Single seat methods all suffer from this problem
and it is even worse for them as they don't even attempt to
compensate.  MMP brings the result closer to a PR result and my issue
is that it doesn't it all the way.

> If the latter, then it seems that the
> right way to compensate is to increase the representation of everyone else.
> You can't rob the independent of his only seat (he would then have no
> representation at all), so you're just left with increasing the relative
> power of the others or of their voters.

A voter for an independent will also be able to vote for a party, so
will be represented by that party.

It is similar to a voter who votes for a local candidate where the
candidate doesn't win the local district.  In that case, his only
representation is on the basis of his party vote.