Dear Kristofer,
if your goal to issue a smaller group representing the same opinions
and debates than the larger group
I think maintaining proportortionality is a good characteristic to make
sure most positions of
these debates survive the attrition. The reduction in size should
facilitate the oral exchanges.
I have a tendancy to view any election as an attempt to build a
microcosm of a larger group
in order to facilitate debates...
For your second point, there is one way to enforce coherency (using a
mathematical definition)
within an MMP election. If one uses the same results to elect the
individual representatives
and to determine the corrected proportion obtained after electing list
members. The simple way to enforce
such coherence between these two proportions is to use a single ballot
MMP, where voting
for an individual is considered too as giving support in favor of this
candate party list.
From what I know two german landers use this system. Otherwise you have
to relie on cultural
honesty of the parties or electorate to avoid the decoy problem.
Salutations,
Stéphane
Kristofer Munsterhjelm a écrit :
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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