[EM] Preferential voting system where a candidate may win multiple seats

[Vidar Wahlberg]

On Fri, Jul 05, 2013 at 11:37:55PM +0200, Kristofer Munsterhjelm wrote:
> I still am not quite sure how it works, because your quotient
> description only refers to the county count, not the national count,
> and I would expect the leveling seats to make use of both.

I'm fairly certain that the national count is only used to determine
whether a party has at least 4% support. After that, only county votes
are used to calculate the quotient, but the quotients for each county
and each party are compared to each other, so that the first leveling
seat goes to the highest quotient on a national basis (then the county
that received the leveling seat is excluded from winning further
leveling seats).

> Each of the three groups can in theory ally with either of the other
> two. This means that, as far as attaining a majority goes, the
> single party-X seat has the same power as either of the two
> coalitions. And that is obviously not desirable. The argument then
> is that if you add in lots of very small parties, any of them might
> become a kingmaker and so get extremely disproportional amounts of
> power.

While I see the point, I think this may be a bit too simplified. Where
as small parties in Norway possibly do have more influence than their
size dictates, they arguably do not have the same power as the larger
parties. There are many factors that weight in here, for example, "SV"
being far left and only willing to cooperate with "AP" (and more or less
"SP") is by many considered the party that came worst out in our current
government. They have no other parties to turn to, the amount of
influence they get depends almost entirely on "AP".
On the other hand, the 3 central parties, "SP", "KrF" and "V" could
potentially cooperate with both blocks, and these can often decide
whether we should have a left-wing or right-wing government. These
parties may gain significant more power than their size dictates, but
history shows that when these small parties are unclear on which block
they want to cooperate with before the election, voters tend to rather
vote for the large party in the voters' preferred block. Seemingly this
was exactly what happened in 2009 when "V" fell below the election
threshold as voters fled to "AP" and "H", as they were unclear on which
block they wanted to cooperate with. This year these central parties are
more clear on which side they're going to cooperate with, but that may
cost them influence, as breaking the promise they've done to their
voters (choosing block) is likely to punish them severely in the future.

> If you're going to remove leveling seats, I would suggest adding
> some other mechanism to make the national count more accurate. I've
> given two ideas of what you might put in its stead: biproportional
> representation (reweighting) or regional-level seats.

While I haven't bothered running the election results for all counties
through Sainte-Laguë where I've removed leveling seat (just increased
directly elected seats by 1), I believe the result would be very close
to the result we already got with leveling seats. In 2009, assuming the
same votes cast, "R" would take a seat from "KrF" in Oslo, and overall
"V" would probably receive some few more seats, mainly the leveling
seats.
I might run the votes through Sainte-Laguë one day, just to see how much
off it would be, but how leveling seats works in Norway, I don't think
the result will be very far off.

> To show how national representation might be inaccurate otherwise,
> I'm going to take an extreme. Consider what would happen if every
> constituency had a single seat. Only the large parties would have
> any chance of winning - and that is what you see in countries like
> the UK. Yet that is the method that focuses most on local
> candidates: the candidate that won got represents that particular
> constituency.

Indeed. By keeping a minimum number of seats per county, and not
changing the districts (as for gerrymandering), this can to a certain
degree be prevented, though. Perhaps this would be difficult to prevent,
if people aren't aware of this and oppose it.

> With multimember districts like Norway, the disproportionality
> wouldn't be quite as bad, but you can still see it taking effect
> when you look at parties that failed to pass the threshold. In going
> from 5.9% support in 2005 to 3.9% support in 2009, the Liberal
> Party, no longer permitted leveling seats, had eight of its ten MPs
> taken away. That is not proportional, and removing leveling seats
> altogether without some other compensation mechanism would only make
> it worse.

Okay, so I bothered to run the election result from 2009 through
Sainte-Laguë after all (real result in parentheses):
            R   |   SV  |   AP  |   SP  |  KrF  |   V   |   H   |  FrP
Akershus: 0 (0) | 1 (1) | 6 (5) | 0 (0) | 0 (1) | 1 (1) | 4 (4) | 4 (4)
A-Agder : 0 (0) | 0 (0) | 2 (1) | 0 (0) | 0 (1) | 0 (0) | 1 (1) | 1 (1)
Buskerud: 0 (0) | 0 (0) | 4 (4) | 0 (1) | 0 (0) | 0 (0) | 2 (2) | 3 (2)
Finnmark: 0 (0) | 0 (0) | 3 (3) | 0 (0) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Hedmark : 0 (0) | 0 (1) | 4 (4) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 2 (1)
Hordalnd: 0 (0) | 1 (1) | 5 (5) | 1 (1) | 1 (1) | 1 (0) | 3 (3) | 3 (4)
MøreRdal: 0 (0) | 0 (0) | 3 (3) | 1 (1) | 1 (1) | 0 (0) | 1 (1) | 3 (3)
Nordland: 0 (0) | 1 (1) | 4 (4) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 3 (3)
Nord-Trd: 0 (0) | 0 (0) | 3 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Oppland : 0 (0) | 0 (1) | 4 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Oslo    : 1 (0) | 2 (2) | 6 (6) | 0 (0) | 0 (1) | 1 (1) | 4 (4) | 3 (3)
Rogaland: 0 (0) | 0 (1) | 3 (3) | 1 (1) | 2 (1) | 0 (0) | 3 (3) | 4 (4)
SognFjor: 0 (0) | 0 (0) | 2 (2) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Sør-Trd : 0 (0) | 1 (1) | 4 (4) | 1 (1) | 0 (1) | 0 (0) | 2 (1) | 2 (2)
Telemark: 0 (0) | 0 (0) | 3 (3) | 0 (0) | 0 (1) | 0 (0) | 1 (1) | 2 (1)
Troms   : 0 (0) | 0 (0) | 3 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 2 (2)
V-Agder : 0 (0) | 0 (1) | 2 (1) | 0 (0) | 1 (1) | 0 (0) | 1 (1) | 2 (2)
Vestfold: 0 (0) | 0 (1) | 3 (3) | 0 (0) | 0 (0) | 0 (0) | 2 (1) | 2 (2)
Østfold : 0 (0) | 0 (0) | 4 (4) | 0 (0) | 0 (1) | 0 (0) | 2 (1) | 3 (3)

Total (169 seats in parliament):
R  :  1 ( 0) seats,  1.3% of national votes,  0.6% ( 0.0%) representation
SV :  6 (11) seats,  6.2% of national votes,  3.6% ( 6.5%) representation
AP : 68 (64) seats, 35.4% of national votes, 40.2% (37.9%) representation
SP : 10 (11) seats,  6.2% of national votes,  5.9% ( 6.5%) representation
KrF:  5 (10) seats,  5.5% of national votes,  3.0% ( 5.9%) representation
V  :  3 ( 2) seats,  3.9% of national votes,  1.8% ( 1.2%) representation
H  : 33 (30) seats, 17.2% of national votes, 19.5% (17.8%) representation
FrP: 43 (41) seats, 22.9% of national votes, 25.4% (24.3%) representation

This was keeping first divisor at 1.4 as it's done in the election. As
expected, parties falling below 4% would get significantly lower
representation than the amount of votes dictates, and the larger parties
benefits from the increased first divisor.

I tried again, setting first divisor to 1.3, but that produced the exact
same result. So finally I tried setting divisor to 1.0 (unmodified
Sainte-Laguë):
            R   |   SV  |   AP  |   SP  |  KrF  |   V   |   H   |  FrP
Akershus: 0 (0) | 1 (1) | 5 (5) | 1 (0) | 0 (1) | 1 (1) | 4 (4) | 4 (4)
A-Agder : 0 (0) | 0 (0) | 1 (1) | 0 (0) | 1 (1) | 0 (0) | 1 (1) | 1 (1)
Buskerud: 0 (0) | 0 (0) | 4 (4) | 1 (1) | 0 (0) | 0 (0) | 2 (2) | 2 (2)
Finnmark: 0 (0) | 0 (0) | 3 (3) | 0 (0) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Hedmark : 0 (0) | 1 (1) | 4 (4) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Hordalnd: 0 (0) | 1 (1) | 5 (5) | 1 (1) | 1 (1) | 1 (0) | 3 (3) | 3 (4)
MøreRdal: 0 (0) | 0 (0) | 3 (3) | 1 (1) | 1 (1) | 0 (0) | 1 (1) | 3 (3)
Nordland: 0 (0) | 1 (1) | 4 (4) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 3 (3)
Nord-Trd: 0 (0) | 0 (0) | 3 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Oppland : 0 (0) | 0 (1) | 4 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Oslo    : 1 (0) | 2 (2) | 6 (6) | 0 (0) | 0 (1) | 1 (1) | 4 (4) | 3 (3)
Rogaland: 0 (0) | 1 (1) | 3 (3) | 1 (1) | 1 (1) | 1 (0) | 3 (3) | 3 (4)
SognFjor: 0 (0) | 0 (0) | 2 (2) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 1 (1)
Sør-Trd : 0 (0) | 1 (1) | 4 (4) | 1 (1) | 0 (1) | 0 (0) | 2 (1) | 2 (2)
Telemark: 0 (0) | 0 (0) | 3 (3) | 0 (0) | 0 (1) | 0 (0) | 1 (1) | 2 (1)
Troms   : 0 (0) | 1 (0) | 2 (3) | 1 (1) | 0 (0) | 0 (0) | 1 (1) | 2 (2)
V-Agder : 0 (0) | 0 (1) | 2 (1) | 0 (0) | 1 (1) | 0 (0) | 1 (1) | 2 (2)
Vestfold: 0 (0) | 0 (1) | 3 (3) | 0 (0) | 0 (0) | 0 (0) | 2 (1) | 2 (2)
Østfold : 0 (0) | 0 (0) | 4 (4) | 0 (0) | 1 (1) | 0 (0) | 1 (1) | 3 (3)

Total (169 seats in parliament):
R  :  1 ( 0) seats,  1.3% of national votes,  0.6% ( 0.0%) representation
SV :  9 (11) seats,  6.2% of national votes,  5.3% ( 6.5%) representation
AP : 65 (64) seats, 35.4% of national votes, 38.5% (37.9%) representation
SP : 12 (11) seats,  6.2% of national votes,  7.1% ( 6.5%) representation
KrF:  6 (10) seats,  5.5% of national votes,  3.6% ( 5.9%) representation
V  :  4 ( 2) seats,  3.9% of national votes,  2.4% ( 1.2%) representation
H  : 32 (30) seats, 17.2% of national votes, 18.9% (17.8%) representation
FrP: 40 (41) seats, 22.9% of national votes, 23.7% (24.3%) representation


The differences were greater than I expected.

With this it's primarily the issue with too few seats in counties that's
causing the larger parties to gain slightly higher representation than
their percentage of the national votes.
On the other hand, the way leveling seats work in Norway, it was
primarily "R" and "V" who ended up below the election threshold who lost
their seats in favour of the parties just above the election threshold.

As I see it, leveling seats should not be necessary as long as there are
enough seats in a county. Granted, if you want absolutely proportional
representation the amount of seats would probably be the amount of
votes, but it should be possible to come acceptably close to correct
proportional representation even with a limited amount of seats.

If leveling seats should be used to even out, then the Norwegian
algorithm is not well suited for this. Leveling seats may as well go to
a party with higher representation percentage than vote percentage, as
long as their quotient in a county is higher than any other party.
It could possibly be improved by considering the national result, and
not just the county result, but I feel leveling seats should be avoided
as it complicates the election method.


Alternatively, instead of running Sainte-Laguë in each county, you could
run SL on the national result (distributing all 169 seats), something
which would produce a representation percentage very close to the actual
result, and then distribute the seats to the parties in the different
counties (keeping the same amount of seats in each county).
I haven't thought out how to distribute the seats in the counties yet,
though.
This way, if it's desirable to set a certain bar to win a seat in the
parliament to prevent too much fragmentation, you could keep the first
divisor greater than 1. It's just the first seat that's affected by
this.


-- 
Regards,
Vidar Wahlberg