[Election-Methods] Matrix voting and cloneproof MMP questions

[Terry Bouricius]

On the question of whether electing a subgroup should be proportional or 
majoritarian...I often make a distinction on two factors: 1) Is the 
association voluntary (in which dissatisfied minorities can easily 
withdraw to join or form a different association), and 2) Is the function 
of the association directional or goal oriented, vs. service, maintenance 
or regulatory-oriented (a political party that wants to move society in a 
direction, vs. an alumni association).

Voluntary associations that have a directional goals (such as  a platform) 
can sometimes be best served by majoritarian or centrist internal election 
method, such as electing party leaders, Whereas compulsory associations 
that are engaged in maintenance (a government) are best served by 
proportional methods.

Terry

----- Original Message ----- 
From: "Kristofer Munsterhjelm" <km-elmet at broadpark.no>
To: "EM" <election-methods at lists.electorama.com>
Sent: Saturday, July 05, 2008 7:09 PM
Subject: [Election-Methods] Matrix voting and cloneproof MMP questions


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 :-)
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