[EM] Mr.SODA

[Jameson Quinn]

Actually, in a perfectly partisan world, you'd want to do this optimization
within each party. Anything like n,n,n will probably be wasting most of its
effort re-confirming that n consists of 2 from party X and 1 from party Y.

So one way to do it would be elect a full sequential slate, then partition
that slate into subsets no bigger than 3 with high mutual correlation within
each subset, then, for each subset, hold the rest of the seats constant,
while finding the optimum 2-3 to take the place of that subset.

But then, that's complicated enough that it's no longer anything like a
"natural" method, but just a (probably less-than-perfect) optimization
algorithm. And so that kinda points back to my original suggestion - anybody
can submit a proposed optimization, and the best one wins. That lets anybody
try any optimization algorithm they want.

JQ

2011/6/20 <fsimmons at pcc.edu>

> ----- Original Message -----
> From: Jameson Quinn
> Date: Sunday, June 19, 2011 7:27 am
> Subject: Re: [EM] Mr.SODA
> To: Kristofer Munsterhjelm
> Cc: fsimmons at pcc.edu, election-methods at lists.electorama.com
>
> > 2011/6/19 Kristofer Munsterhjelm
> >
> > > fsimmons at pcc.edu wrote:
> > >
> > >> In the discussion of a proportional representation version of
> > SODA it
> > >> was lamented that the non- sequential version of PAV was
> > >> computationally hard, and was suggested to make use of the
> > PAV measure of
> > >> goodness to pick the winning slate from all of the slates
> > >> that anybody cared to nominate.
> > >>
> > >> While that would certainly be feasible and very likely near
> > optimal,>> another possibility is to use non- sequential PAV to
> > choose the first
> > >> three members of the slate, and then choose the remaining members
> > >> sequentially, conditioned on the membership of the first
> > three as
> > >> well as those chosen subsequently.
> > >>
> > >> The number of slates of size three is only n*(n-1)*(n-2)/6 , which
> > >> is less than five million when there are (n=)three hundred
> > >> candidates.
> > >>
> > >> If the members of the senate were chosen this way, the first three
> > >> could be a kind of triumvirate presidency of the senate.
> > >>
> > >
> > > You could also do this to get a hybrid of sequential and non-
> > sequential> PAV. Decide on a chunk size k, then you calculate
> > the first k winners
> > > non-sequentially (n choose k for n candidates). Lock these
> > (i.e. decide
> > > they'll win), then try every council of size min(k*2, desired
> > size) with
> > > these locked. Then min(k*3, desired size), min(k*4, desired
> > size), etc,
> > > until you have elected as many as you want.
> > >
> > > Sequential PAV is just this kind of PAV with k=1. k=2 or k=3
> > should be
> > > feasible even with very large values of n, and would
> > approximate true
> > > PAV better than would ordinary sequential PAV.
> > >
> > > So, for instance, if you want to elect eight winners out of A-
> > Z with
> > > k=3, you'd first do
> > >
> > > elect ??? -> say the optimum here is ABC, then
> > > elect ABC??? -> say the optimum is ABCDFG, then
> > > elect ABCDFG?? -> say the optimum is ABCDFGKQ, and then that's your
> > > outcome.
> > >
> > >
> > >
> > I like this idea, but instead of electing 3,3,2 in this example
> > as you
> > suggest, you should elect 2,3,3 (that is, AB, CDF, GKQ, assuming
> > it comes
> > out the same, which it usually would). That concentrates the broadest
> > optimization nearer to the threshold, where it matters more. (In
> > fact, you'd
> > probably get the same results with less computing effort by electing
> > 1,1,1,1,1,3).
> >
> > JQ
> >
>
> Great idea, Kristofer.
>
> How about 3, 2, 3?  Wouldn't this give better balance?
>
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