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

[Vidar Wahlberg]

On Fri, Jul 19, 2013 at 08:23:04AM +0300, Juho Laatu wrote:
>> I do feel that distributing first seats to small parties first makes
>> more sense, especially considering that certain small parties (such as
>> "Rødt") got a lot of support in districts with large cities, but nearly
>> no support in other districts. They should be "guaranteed" to receive
>> their won seats in the districts where they got most support.
> 
> I think it is ok to simply distribute first all seats of the smallest party, then all seats of the next smallest party etc. This is to avoid any weird results where some parties got seats in districts where they had relatively small support. Large parties do have strong candidates in every district, so leaving the "rounding errors" to them causes least harm.

I actually tried something not too far from this, I distributed one and
one seat to each party, i.e. in a election where 3 parties won seats:
party A gets a seat
party B gets a seat
Party C gets a seat
Party A gets a seat
...
When a party had no more seats they were of course skipped. What
happened was that certain districts got very peculiar results for the
large parties. For example in Oslo all the small parties got one or more
seats, leaving few seats left for the largest party, who got half the
amount of seats you'd expect compared to their vote percentage in that
district.
This is why I went for the slightly more complex way of distributing
seats in the reversed order the seats were won. It does mean that both
small and large parties suffer rounding errors, but it's more evenly
spread, and with a slight advantage to smaller parties.


The biproportional apportionment system Kristoffer linked to is very
interesting. It is slightly more complex and I fear it may be too
complex for common people to understand (which will make it difficult to
gain support for it), and I wonder if it may end up with exceptionally
long calculation time when there are many districts and many parties.
Especially in Norway where amount of seats in a district may be
radically different from the amount of votes cast in that district.
Finnmark is a such example, which got a low population and few voters,
but a large area, giving them relatively many seats (calculated by
population and area) compared to amount of votes. As I've understood the
algorithm so far it'll calculate how many seats each party wins in a
district purely based on percentage of the votes cast there, then later
adjusted up or down to match the real amount of seats that should be won
in the district. Due to the low amount of votes in this district it's
likely that only about 1-2 seats will initially be won there, meaning
you'll have to weight up the votes in Finnmark and weight the votes down
in another district.

I'd like to try implementing it, but I don't fully grasp all of it yet
and most of my spare time ran out, so it might take a while.


-- 
Regards,
Vidar Wahlberg