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

[Kristofer Munsterhjelm]

On 07/04/2013 08:39 PM, Vidar Wahlberg wrote:
> On Thu, Jul 04, 2013 at 07:18:18PM +0300, Juho Laatu wrote:
>>> That doesn't sound so different from leveling seats. In the
>>> Norwegian system, you give each county an extra seat, but this
>>> seat is assigned based on the difference betweeen the seats so
>>> far allocated (on county by county basis) and the national
>>> apportionment. I'm not sure how the algorithm decides which
>>> county gets which party's seats, but it's not a simple
>>> biproportional thing.
>>
>> Yes, the end result is probably very similar. The fact that each
>> leveling seat is tied to one county further reduces the difference
>> (since there are no "countyless" seats).
>
> About the Norwegian leveling seat algorithm: The leveling seats goes
> to the party (with at least 4% of the national votes) with the
> highest quotient. Once a party in a county has received a leveling
> seat, that county may not receive any more leveling seats. The
> quotient is calculated as following: (party_county_votes /
> (party_county_seats * 2 + 1) / (county_votes / county_seats)
> "county_seats" does not include the leveling seat. Since each county
> receives 1 leveling seat the result would be fairly close to just
> increasing the amount of seats in the county by one, but smaller
> parties who haven't received any seats at all in the county (but got
> at least 4% of the national votes) have a slight advantage with the
> leveling seat algorithm as the algorithm use 1 instead of 1.4 as the
> first divisor.

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.

But I think I see the general outline: the discrepancy is calculated in 
terms of national seats that "ought" to have been achieved, per party, 
minus the number of seats actually achieved, and then the spare seats 
are given to parties to bring the two counts more in line with each 
other, in such a way that the parties that were closest to getting an 
extra seat anyway (if that's what the quotient does) will get them.

If so, it's not that different from the biproportional representation 
algorithm, but it still feels less intuitive than it. Hm, again I would 
have to think about it further...

> As for the election threshold, I completely agree with Juho, also
> minorities should be represented in the parliament. I've never
> really understood the argument that an increase in parties
> represented in the parliament will lead to chaos. How the election
> threshold work in Norway, that's not really what's preventing other
> parties to be represented (that we're using 1.4 as the first divisor
> in Sainte-Laguë is what's making it difficult for smaller parties to
> get a foothold).

I think the argument goes that because the system is based on parties, 
the various parties will act like unified blocs. Therefore, the actual 
power in parliament will be closer to Banzhaf's power indices than the 
fraction of the seats held by any given party.

As an extreme, say you have two coalitions: a left-wing and a right-wing 
coalition. They're evenly matched (say 84 seats each). Then the last 
seat is held by a party with low support (party X).

To attain majority, these combinations are theoretically possible:

Left-wing bloc + party X
Left-wing bloc + right-wing bloc
Right-wing bloc + party X

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.

I'm not sure I agree with it, but I can *understand* the argument. The 
worries could be alleviated by somehow making party discipline less 
strict so that it's harder for the parties to rule over their MPs, but I 
don't know how to do that. Another option is to make minority rule the 
default so that the "coalitions" shift according to the law or policy 
being considered. But some would consider that more chaotic in another 
manner.

>> I favour systems that are so simple that regular voters can easily
>> understand how they work.
>
> Even though I'm a fan of Ranked Pairs & Condorcet methods, I too
> share this sentiment. Another argument could be that voters probably
> would be wary of drastically changing the existing voting system. In
> the Norwegian voting system, changing it by removing election
> threshold, increase seats in each county by 1 and remove leveling
> seats, and possibly reduce the first Sainte-Laguë divisor slightly,
> say 1.3, while making it possible for voters to rank parties, could
> greatly help prevent the fear of "wasting" ones vote. Using the
> counting method mentioned earlier (exclude party with fewest votes,
> rerun Sainte-Laguë until all remaining parties got at least 1 seat),
> it's arguably easier to explain than the current one with the
> leveling seat algorithm.
>
> It wouldn't help on the "I can't vote on my favourite party because
> they [may] cooperate with a party which I don't like", but that's
> arguably more of an issue with the parliament (or the people) than
> the voting system, so that's a bit out of scope here.

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.

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.

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.