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

Vidar Wahlberg canidae at exent.net
Fri Jun 28 06:04:13 PDT 2013

On Fri, Jun 28, 2013 at 12:51:02PM +0200, Kristofer Munsterhjelm wrote:
> I don't have proof that it wouldn't degenerate into a raw populist
> competition, though, so I can certainly see your point. I just don't
> know of any examples of STV-like methods failing or leading to raw
> populism in the countries where they're used.

Likewise, I don't have any proof that it will degenerate into a populist
competition, but I do see the potential that it will, when you vote
directly for a person rather than a party. I strongly suspect that
people will vote for highly charismatic people which may not reflect
their political skill.
The abstraction layer of letting a party order the list may result in
more experienced politicians at top, but this is purely a theory, I have
no evidence to support it.

> When used as a party list method, ordinary STV reduces to largest
> remainder party list with a Droop quota. So if that's what you want,
> just use largest remainder.

Intriguing, obviously this is what I've done, but instead of running x
cycles to allocate one and one seat for those above the quota I just did
a shortcut allocating n seats in one cycle. I'm surprised how something
as obvious as this flew by me, thanks for pointing it out!

> But that wouldn't fix the unfairness in Norwegian party allocations
> either. I think your footnote #2 is closer to the mark, and the
> unfairness (while much slighter than in the US, obviously) has three
> parts. The three parts are the leveling seat algorithm, how the
> party list method acts when there are few seats, and the threshold.

It may have been implied, but I would also add that the lack of ranking
parties in your vote is the bigger contributor to the unfairness. In
2009, "Rødt" (for those not familiar with Norwegian parties: "Rødt" is a
radical left-wing oriented party) was 1083 votes from gaining a seat for
Oslo county, instead the last seat went to "Høyre" (conservative
right-wing oriented party). I'm fairly sure you'll agree with me that
those 12917 people who voted for "Rødt" most likely would rather see
that last seat go to someone else. If those people instead had voted for
"SV" (left-wing, close to "Rødt"), that would be more than enough to
take that seat from "Høyre" and give it to "SV".

> I've never quite understood how the leveling seat algorithm works,
> and it often produces counterintuitive results. I think it would be
> better to just have "regional seats" that belong to a region rather
> than to a county. One would then apportion the local seats, and
> afterwards compare the results for a region with the results that
> region "should" have, giving out regional seats to compensate. The
> only problem with that scheme is to find out where the regional
> seats should be located, and from which list/s the regional MPs
> should be drawn.

The leveling seat algorithm is... peculiar. It's some time since I read
up on it, but one thing I do recall was the ambiguous explanation on
where these seats are to be distributed. As you probably know there were
fewer leveling seats (8) some years ago (1989-2005), but this was later
changed to "one leveling seat per county". When there was 8 then not all
counties would get a leveling seat, but rather the county where a party
above the election threshold were nearest to receive a directly
appointed seat. Now that there are 19 leveling seats it seems to be that
each county gets its very own leveling seat, but as far as I remember
the rules, it doesn't actually say that each county gets 1 leveling
seat. Infact as I understood the rules one county could get multiple
leveling seats, for instance if it had two parties above the election
threshold, where both parties where very close to get a directly
appointed seat. This is obviously not how it's done, each county do get
one leveling seat, but this is not explained well in the rules.
I'm derailing here, returning to the subject.

> As for how the party list method acts when there are few seats, this
> is probably closer to the problem you're seeing (when one disregards
> leveling seats). Here's an old example I often pull in similar
> cases:
> 46: L > C > R
> 44: R > C > L
> 10: C > R > L
> In the extreme case of there being only one seat, you would want C
> to win. But every divisor method reduces to Plurality when there's
> only one seat, so L gets elected instead. On the other hand, if you
> have a thousand seats, proportional representation pretty much says
> you should give 46% of them to L (were it a party), 44% to R, and
> 10% to C.
> So we'd like a method that is Condorcetian when there's only one
> seat, yet proportional when there are loads. And such methods exist.
> Schulze's proportional ordering method comes to mind. It's complex,
> however, and it might be possible to make simpler methods since we
> can elect each "candidate" (party) multiple times.

This gave me an idea.
We seem to agree that it's notably the exclusion part that may end up
excluding a party that is preferred by many, but just isn't their first
I'm sticking to quota election because I don't fully grasp how to apply
other methods (Sainte-Laguë, for instance) to determine when to start
excluding parties.
1. Give seats to parties exceeding the quota (seats = votes / quota)
2. Create an ordered list using Ranked Pairs/Beatpath, exclude the least
   preferred party and redistribute its votes. Repeat.

Using your example above, since neither L, C nor R reach the quota, you
would order them using i.e. Ranked Pairs. A quick glance tells me that
the order would be C > R > L, L is excluded and its votes goes to C.
New tally would give C 56 votes which would be enough to win the
election (exceeding the quota).

Any thoughts on this?

Sorry about not commenting on the rest of your reply, I read it with
interest, although I'd like to get rid of both leveling seats and
election threshold. The goals behind these concepts I feel are well met
with a preferential election (with the exception of fragmentation, but
that is a fairly poor argument, as I believe only "Rødt" would be the
new addition to the parliament if it wasn't for these aspects of our
voting system).

Vidar Wahlberg

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