[EM] Biproportional representation (was Re: Preferential voting system where a candidate may win multiple seats)

[Vidar Wahlberg]

On Mon, Jul 22, 2013 at 10:49:52PM +0200, Kristofer Munsterhjelm wrote:
> To make the biproportional voting method work, the numbers should be
> set so that the rows give the correct allocation per party and the
> columns give the correct allocation per district (or vice versa,
> depending on what you assign to the rows and columns). So I think
> the simplest way to do so would be to apply the weighting to the
> vote numbers themselves to get "effective votes".

A significant drawback with weighting votes is that it will likely lead
to an outcry of protests ("why is my vote here in Oslo only worth half
of a vote in Finnmark?"). Arguably this is already the case, but it's
disguised so people are most likely not aware of it.
Something like this may be required though, as there's a theoretical
possibility that a party can win a seat that can't be assigned to the
party in any district:
In Oslo there are 17 seats. Since Oslo is a small region with high
population, votes there are weighted less than votes in for example
Finnmark. If 18 parties enters the election with a party list only in
Oslo, and these 18 parties win all the votes, evenly distributed among
themselves, then deciding party seat amount based purely on votes with
equal weighting is likely to give all these 18 parties one or more
seats. There are not enough seats in Oslo for these parties, and the
parties have no candidates who can fill the seat in any other region.
Perhaps this scenario is as unlikely as two larger parties getting the
exact same amount of votes (which I'm not sure how is dealt with in
Norway), but it should nevertheless be adressed.
Partly the idea behind all of this was to make every vote weighted
equally when it comes to party proportionality, while keeping the
possibility of giving certain regions a larger or smaller amount of
the seats than their vote percentage dictates.

I must admit, the more I look into this algorithm, the less enthusiastic
I feel about it. Let me try to explain:
It appears to be quite complex, even more so when regional seats are
predetermined and not based on votes (unlike it is in the example at
Wikipedia[1]). I find the explanation of the method difficult to
understand, and I don't think it'll be any easier to explain how it
roughly works to the general public. As we've discussed earlier, a
method is more likely to be accepted if people understand it.

Implementing it is no easy task. It may be that my sources, mainly the
Wikipedia entry and Olli Salmi's page[2] are a bit short on the topic,
but one hindrance I've faced is figuring out what the divisor values
should be during the correction stages. Neither sources elaborate well
on how they decided the divisor values, and Salmi writes "I have just
fiddled with the divisor until the total number of seats assigned is
correct", but that's no good when implementing the algorithm.

The end result does not seem to be greatly different compared to
distributing seats using algorithms discussed earlier, such as using a
quota to determine seats won for certain and distribute remaining seats
to "largest remainder" which Juho suggested, or just distributing all
seats to "largest remainder" in the reversed order the seats were won as
I suggested earlier. If these ideas are flawed and/or can produce
peculiar results I'd appreciate feedback.


[1]: http://en.wikipedia.org/wiki/Biproportional_apportionment
[2]: http://www.uusikaupunki.fi/~olsalmi/vaalit/Biproportional_Elections.html


-- 
Regards,
Vidar Wahlberg