[Election-Methods] Matrix voting and cloneproof MMP questions

[Juho]

Few notes.

In some cases having an opposition may be a positive thing. E.g.  
having always the same government may not be a good thing in the long  
run.

One approach is to use some single winner method to determine the  
preferred coalition that should form the government (I'm assuming a  
multi-party system here) (candidates in the single winner election  
are coalitions like "Party1+Party2", "Party1+Party3+Party4" etc.).  
That could lead to either a majority or a minority government,  
consisting of one, few or all parties.

Juho


On Jul 7, 2008, at 2:07 , Terry Bouricius wrote:

> 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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>
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