[Election-Methods] Matrix voting and cloneproof MMP questions

[Kristofer Munsterhjelm]

I thought I could ask a few questions while otherwise being busy making 
my next simulator version :-) So here goes..

First, when a group elects a smaller group (as a parliament might do 
with a government, although real parliaments don't do it this way), 
should the method used to elect the smaller group be proportional?

I think one could make a majoritarian version with cardinal 
ratings/Range. It'd work this way: for n positions, each voter submits n 
rated ballots. Then, with k candidates, make a k*n matrix, where 
position (a,b) is the sum of the ratings the voter assigned candidate a 
in the ballot for position b.

We've now reduced the problem of picking (candidate, position) values so 
that the sum is maximized. The constraints on the problem are: only one 
value can be selected from each row (can't have the same candidate for 
two positions), and only one value can be selected from each column 
(can't have two candidates for the same position). I think that's 
solvable in polynomial time, but I haven't worked out the details.

That's for majoritarian matrix votes with cardinal ratings (or Range - 
could also be median or whatever as long as the scores are commensurable).

(On a related note, has anyone tried to use Range with LeGrand's 
Equilibrium Average instead of plain average?)

Perhaps the same pick-the-best-sum reasoning could be extended to a 
Condorcetian matrix vote, using Kemeny score for the Condorcet matrix 
for the position in question instead of ratings sums/averages. But as 
far as I remember, Kemeny scores relate to social orderings, not just 
candidate choices, so maybe the Dodgson score instead -- but that may 
not be comparable in cases where different candidates are Condorcet 
winners in different elections, since those would all have Dodgson 
scores of 0 (no swapping required).

In any case, the reduction above won't work if matrix voting methods 
ought to be proportional. I'm not sure whether it should be majoritarian 
or proportional, and one could argue for either - majoritarianism in 
that that's how real world parliamentary governments are formed 
(negotiations notwithstanding), and proportionality because some group 
may be very good at distinguishing suitable foreign ministers while some 
other, slightly larger group, might not do very well at that task but be 
good at distinguish suitable ministers of interior.


Second, I've been reading about the "decoy list" problem in mixed member 
proportionality. The strategy exists because the method can't do 
anything when a party doesn't have any list votes to compensate for 
constituency disproportionality. Thus, "cloning" (or should it be called 
splitting?) a party into two parties, one for the constituency 
candidates, and one for the list, pays off. But is it possible to make a 
sort of MMP where that strategy doesn't work?

That MMP method would have to use some kind of reweighting for those 
voters who got their way with regards to the constituency members, I 
think, because if the method just tries to find correlated parties, the 
party could theoretically execute the strategy by running all the 
constituency candidates as independents.
What kind of reweighting would that be? One idea would be to have a rule 
that says "those with say x about the constituency vote gets 1-x in the 
list vote". Then vary x until the point of party proportionality is 
found. No matter what party someone who makes a difference with regards 
to the constituency candidate chooses, his vote loses power 
proportionally, and thus decoy lists wouldn't work.

No concrete methods here, but maybe someone else will add to them... or 
find flaws in my reasoning and correct them :-)