[EM] Preferential Party-List Proportional Representation (PPLPR)

[Juho Laatu]

On 08 Nov 2014, at 17:43, Vidar Wahlberg <canidae at exent.net> wrote:

> On Sat, Nov 08, 2014 at 03:18:45PM +0000, Toby Pereira wrote:
>> 50%: L>C
>> 50%: R
>> 
>> Then the seat allocation would be:
>> 
>> L; 50%
>> C: 12.5%
>> R: 37.5%
>> 
>> The second preference of C causes too much of an encroachment into the R allocation. All STV methods would give R 50% of the seats and I would say your method gives disproportional results. What advantages would you say your method has?
> 
> Quick answer, as I'm heading out:
> Yes, with three parties and two dominating, you could indeed see a
> significant encroachment into other parties. This is however usually not
> the case in party list elections, there tends to be significantly more
> parties. As the amount of parties increase, the encroachment decrease.
> 
> Also, consider this example:
> 100 A>B>C>D>E
>  1 B>C>D>E>A
> 100 C>B>D>E>A
> 100 D>B>E>A>C
> 100 E>B>A>C>D
> 
> Every single voter rank B high, but an STV election would likely not
> give B a single seat, because very few have B as their first preference.

I noted in one of my earlier mails that PPLPR can be said to introduce a new category of methods. The idea seems to be to give some "additional" seats to some good compromise parties. Traditional PR on the other hand works so that all groups can elect their (as exact as possible) proportional share of the representatives. They can elect exactly those candidates that they consdider best (i.e. never mind what others say about them as long as the party supporters think they are the best). In line with this PR tardition, if there were four seats in this election, it would look obvious that they should go to A, C, D and E, since this allocation leaves only one voter without a representative, and all the large parties get just marginally (= worth 0.25 votes) more representatives than they have support. There may not be any official definition of traditional PR, but I think this is about how it is supposed to work, i.e. all groups can get their proportional share of representaives that most accurately reflect their opinions.

> I consider this a fundamental flaw with STV/IRV style elections, and
> something Condorcet methods (and cardinal methods) handle better.

Yes, at least Condorcet tries to elect a compromise candidate, and that candidate could come from a small party. In the example above B is a Condorcet winner.

We could also combine the Condorcet style compromise candidate idea and the traditional PR idea (i.e. without going all the way to the more radical compromise oriented approach of PPLPR). Maybe we would first elect all the non-fractional seats in the tarditional way. This would already offer pretty good traditional PR. If there are 9 seats, each large party (A, C, D, E) will get 2 seats right away. There is one more seat left to allocate to someone. Now we could, in order to find the beast possible PR, take the second preferences into account. All the large parties have 10.9 votes left (=100-2*401/9). Party B has 1 vote left. Also with these new weights, B is still the Condorcet winner, and could be elected as the ninth representative although it still has clearly less unused votes than the large parties. That can be said to be more proportional than electing one of the large party representatives. All the big parties at least prefer giving the last seat to B instead of to some of the other large parties. Most traditional PR methods (that do not see the second preferences) would give the last seat to one of the large parties.

This is thus how we could combine the traditional PR style and Condorcet style compromise orientation in the allocation of the last fractional seats. Things get a bit more complex if there are more than one seat left when we start the compromise style allocation of the last seats. I'll skip that discussion for now.

Juho


> 
> 
> -- 
> Regards,
> Vidar Wahlberg
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