[Election-Methods] Determining representativeness of multiwinner methods

[Juho]

On Jun 27, 2008, at 13:54 , Kristofer Munsterhjelm wrote:

>> That could be one big poster where the candidates are listed on  
>> the right hand side and the left hand side is used for  
>> representing the tree structure (and the names of the parties and  
>> the subgroups).
>
> That could work, at least in cases where there's only one district  
> and the party limits the depth of the tree so it doesn't get too  
> cluttered. I don't think it would be of much use in small-district  
> elections, since either all subgroups would have to field  
> candidates (making the regional lists very long), or only some  
> subgroups would have candidates you could vote on.
>
> To be absolutely safe, each party in party list PR would have to  
> have at least as many candidates in the running for a region as  
> there are seats in the region. If you want absolute representation  
> not just between parties but within the party, each subgroup would  
> have to do the same, which would add greatly to the count.

If needed some sensible limits could be set for each party, e.g. 5 +  
1.5 * number_of_current_representatives.

> It could be solvable by something like MMP where you have one  
> constituency (FPTP or STV) vote and one subgroup vote, where the  
> subgroup totals propagate up the party -- or for an asset-flavored  
> method, the subgroups negotiate with weighted votes as to how the  
> list votes are to be divided up.

My default basic method is simply an open list method with hierarchy.  
The number of votes to individual candidates accumulates to subgroups  
and parties. Seats will be allocated starting from the root of the  
tree in reverse direction. My default assumption for regional  
proportionality is to have districts that have multiple seats. It is  
possible to distribute the seats country wide in the political  
hierarchy and at the same time make sure that also the regional  
proportionality requirements are met (in Finland there is a reform  
process going on at the moment, planning to move from the traditional  
open list based system in this direction).

> Asset-flavored methods would have the same Fiji-type problems you  
> referred to, however, if the candidates throw their weight behind  
> something you don't support. One might say that feedback would make  
> the voter trust the candidate less the next time around and thus  
> keep them in line, but that argument could be made for Fiji, too,  
> and observation shows that feedback isn't strong enough.
>
>>> The substituted ranks (candidate-individual automatic how-to-vote  
>>> cards) would nest outwards, from the small wings to the  
>>> increasingly larger ones within the party itself, then on to  
>>> other parties in preference. In a sense, they are "lists" of  
>>> their own, and so the problem isn't completely avoided.
>> Are there some specific cases where the tree like inheritance  
>> order is clearly not sufficient?
>
> Not really - it was more of an addon to increase the information  
> given, with the idea that if the candidates transfer beyond their  
> own party, then a socialist green could favor other socialist and  
> green parties over conservative ones, for instance. Since I  
> considered the tree-structure too complex, I thought that  
> complexity wouldn't be an issue.
>
> At least the rank substitution method gives a simple way of  
> implementing such a nested party-list method. If candidates declare  
> subgroups, and subgroups supergroups, then the rank votes are  
> generated so that a list gives the ordering within subgroups, and  
> then the ranked vote is [Candidates in subgroup] > [ Candidates in  
> other subgroups ] > [ Candidates in other supergroups ] and so on.
>
> That brings us to the original question, whether it'd be possible  
> to simulate this method. If "tree-based party list" (as we may call  
> it) is transformed to STV, then any question of proportionality of  
> tree-based party list would be reduced to a subset of the questions  
> of proportionality of STV alone, and so it wouldn't be necessary to  
> test tree-based party list separately - at least not unless the  
> structure mitigates some problem with ordinary STV representation.

The three / nested party-list style is a more limited version of the  
rank substitution style (the inheritance network is limited to form a  
tree structure). STV (unlike the previous ones, I guess) allows the  
voter to determine the inheritance order (and is therefore even less  
limited).

The more complex methods can simulate the simpler methods. The simple  
ones have the benefit of simplicity (easy to vote, easy to understand  
the position of the candidates, no need to check and compare the  
opinions of numerous candidates). The complex ones allow voters to be  
more expressive. The problem of the complex methods is complexity,  
e.g. in STV one would need to cast a quite complex vote to simulate  
the tree model => C1>S1=S2=S3>P1=P2=P3=...=P20>A1=A2=...=A50  
(C=Candidate S=Subgroup P=Party A=Alliance). (One could of course  
introduce also names for the groupings =>  
C1>Subgroup4>Party2>Alliance3.)

One possible voting pattern that the tree inheritance doesn't support  
is Mybestfriend>Myparty where my friend does not represent my party.  
But this is quite marginal when thinking about the outcome of the  
election.

Another pattern that you also referred to is to have interest in  
supporting all greenish candidates irrespective of which party they  
represent. Already the tree structure does most of the job by  
guaranteeing that the green branch of my party will get my vote. But  
if there are many greenish separate branches in different parties the  
rounding errors might lead to not guaranteeing a fully proportional  
result. I already discussed above the possibility of providing  
simultaneously both political and regional proportionality. In  
principle it is possible to add also other proportionalities in the  
equation, e.g. greenness (depends on the number of votes given to the  
green candidates) and sex (could be based on a fixed 50-50 split).  
Too many details/proportionalities add some rounding related problems  
in the seat distribution method.

The three structure may be sufficient for most typical needs. To my  
understanding many people like STV more than lists (closed, open)  
since it allows the voters to have full freedom from the party  
structure, and freedom from the parties determining the order of the  
candidates (closed lists). Also the tree style is considerably more  
flexible than the typical monolithic party structure that is commonly  
used today (allows voters to determine the internal opinion and  
direction of the parties).

Juho


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