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

[Vidar Wahlberg]

On Fri, Jun 28, 2013 at 03:04:13PM +0200, Vidar Wahlberg wrote:
> This gave me an idea.
> We seem to agree that it's notably the exclusion part that may end up
> excluding a party that is preferred by many, but just isn't their first
> preference.
> I'm sticking to quota election because I don't fully grasp how to apply
> other methods (Sainte-Laguë, for instance) to determine when to start
> excluding parties.
> 1. Give seats to parties exceeding the quota (seats = votes / quota)
> 2. Create an ordered list using Ranked Pairs/Beatpath, exclude the least
>    preferred party and redistribute its votes. Repeat.

Chris, Kristofer.
Spending the rest of the day on this, I think I finally understood what
you meant with "best formula for apportioning seats in List PR". Or at
least I eventually came up with a very simple method, even though it
does not meet my concerns about excluding a second preference party that
is far more popular than a party that have some more first preference
voters.
For larger parties who are very likely to get a seat there's neither any
reason to create an ordered list, as those parties who do receive one or
more seats will never have any votes transfered.

Basically, this is what I do:
1. Distribute seats using Sainte-Laguë.
2. If any parties received no seats, exclude the party with least votes
   and redistribute votes to 2nd preference.
3. Repeat 1-2 until all non-excluded parties got at least 1 seat.

Although as noted a party that is a popular as second preference (but
less popular as first preference) will easily be excluded, even though
more voters would prefer this party over another party.

I did implement the other idea I had, setting a quota, distributing
seats with "seats = votes / quota" and then redistribute the votes from
the least popular party (found using an inversed RP, ranking preference
from least to most preferable), regardless of whether the party had
received seats or not.
It was quite interesting, but there's at least one very unfortunate
effect: It could benefit a party to instruct its voters not to set up a
party whose voters are likely to set the other party as second
preference.
For example, party A knowing that voters of party B are likely to put
party A as second preference could benefit from having party B excluded
early, and thus encourage their voters not to put party B in their
preference list. This can of course backfire, leading to neither of the
parties winning an extra seat, in the cases where party A are to be
excluded before party B.

So I'm left with two systems now. One conceptually very simple system
that is quite similar to the voting system already used, but a system
that won't reflect the preference of the voters very well, only the
voters of parties that won't get a seat will have their preference
heard.
And one system that's far more complex and possibly more open for
tactical voting, but reflects the preference of the voters better as the
preference of all voters will be heard.


-- 
Regards,
Vidar Wahlberg