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

[Juho Laatu]

On 18.7.2013, at 21.13, Vidar Wahlberg wrote:

> For each district and each party, calculate the quotient.
> Quotient = partyDistrictVotes / (2 * partyDistrictSeats + 1)

In the category of simple and straight forward algorithms, here is one approach.

- first use SL to determine at national level the number of seats that each party gets
- then allocate all seats of the smallest party so that it gets it seats in districts where it has full nationalQuota of votes, or largest fractional nationalQuota of votes
- continue with the next smallest party etc.
- nationalQuota = nationalVotes / nationalSeats
- after all seats of some district have been allocated, that district will be ignored when counting the rest of the results
- if some party doesn't have sufficient number of candidates in some district, restart the algorithm but reduce the number of seats of this party by one

I think the last row where a party loses a seat if it doesn't have sufficient number of candidates in all districts is fair since it is usually a mistake of the party if it does not nominate many enough candidates. (In the recent proposal in Finland they did some backtracking in such cases, but to me that seemed like adding unnecessary complexity to the method without getting any real benefits.)

(One could also adjust the use of nationalQuota in the districts so that the impact of different voting activity in each district is cancelled => districtQuota = districtVotes / districtSeats, or maybe even something more complex (and possibly more fair).)

> it's possible to keep the
> modified Sainte-Laguë (first divisor is 1.4 instead of 1) if one so
> desires

I note that in addition to being a threshold to small parties, divisor 1.4 can be also used to avoid strategic splitting of a small party to two even smaller parties to get two seats instead of only one. Generally I don't like thresholds at all since they make the results less proportional, but I can accept this one if the risk of startegies is real.

Juho