[Election-Methods] Determining representativeness of multiwinner methods

[Kristofer Munsterhjelm]

> 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.

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.

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.