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

[Vidar Wahlberg]

On Thu, Jul 18, 2013 at 08:48:28AM +0300, Juho Laatu wrote:
> On 18.7.2013, at 3.11, Vidar Wahlberg wrote:
> 
>>   so the party gets
>>   the seat in the district with the highest:
>>   partyVotePercent / (2 * partyDistrictSeats + 1)
> 
> Will the size of the district impact the results? (i.e. 20% of the votes in a district that has 6 seats altogether should always give that party at least one seat, but if that district has only 3 seats, getting a seat would not be certain)

The size of the district will not affect the order of distributing the
seats, it's only the percentage of the votes the party received in the
district that plays a role. There's no guarantee that a party with 20%
of the votes in a 6-seat district receives at least 1 seat, it entirely
depends on that party's seat allocation in other districts, and other
parties seat allocation in this district. It is however very likely that
the party will receive at least 1 seat in the district, but here's a
scenario where it wouldn't receive a seat in that district:
6 smaller parties win at least 1 seat each. As it happens all these 6
parties got the highest percentage of the votes in this district, and
since the distribution of seats favour giving the first seats to the
smaller parties, the small parties will all receive their first seat in
this district, leaving no available seats to larger parties.

It could be an idea to implement an algorithm that tries to minimize
"partySeatsInDistrict / seatsInDistrict - partyPercentageInDistrict" for
all parties in all districts, but I believe this is a fairly difficult
problem to solve, and the algorithm would likely be complex.

Alternatively you could go the other way, distribute seats to parties in
district the same order they won the seats, but then you'll get the
opposite effect, that small parties may not win a seat in a district
where they got 10% of the votes (because the larger parties took all the
seats), but rather get a seat in a district where they got 1% of the
votes.
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 wouldn't oppose a better algorithm at distributing seats to districts,
but this method is simple and acceptably accurate (it's arguably no
worse than todays algorithm with leveling seats), and I believe it's
important that the method is so simple that most people can easily grasp
it.

>> Once a district received all its seats, it's of course excluded from
>> receiving any more seats.
> 
> I guess the same applies to districts. Once all the seats of a district are gone, the remaining (party) seats will be allocated in other districts.

I think you may have misread the line you quoted.
Since you basically assign seats in the opposite order the seats were
won, you don't have the problem that a party would get more seats
assigned than they won. This is only a problem for districts.


-- 
Regards,
Vidar Wahlberg