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

[Juho Laatu]

On 21.7.2013, at 14.42, Vidar Wahlberg wrote:

> 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.

Yes, it is possible and even typical that many small parties get their best results in the same district. One simple fix (and one step more complex algorithm) is to allocate full quota seats first and fractional seats only after them. This means that the results can be off only by less than one quota for each party in each region. (Also other more ideal methods can be developed.) I wonder if accuracy of one quota would be sufficient.

> 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.

Yes, it has some complexity problems. Of course the benefit is that the results will follow some ideal definition. I guess the society and politicians have a lot to say on what approach is best.

> 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.

It would be good if there was an EM algorithm library somewhere. This has been discussed also before. I guess the rich environment of languages and platforms is one key reason why such nice library culture does not exist (not in EM, not much elsewhere either). Hoping for a better future with ability to communicate also easily implementable algorithms.

Juho


> 
> 
> -- 
> Regards,
> Vidar Wahlberg
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info