[Election-Methods] Matrix voting and cloneproof MMP questions

[Stéphane Rouillon]

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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