[EM] Centrist vs. non-Centrists (was A distance based method)

[Jameson Quinn]

2011/7/13 <fsimmons at pcc.edu>

> Jameson, I'm surprised that you consider a Condorcet method to be too
> extremist or apt to suffer center
> squeeze.
>

Hmm... you're right, I hadn't recognized that your "remove one of closest
pair" method was Condorcet-compliant, as any pairwise method.

>
> Think Yee diagrams; all Condorcet methods yield identical diagrams, while
> center squeeze shows up
> clearly in methods that allow it.
>
> Of course if we have a multiwinner method, we don't want all of the winners
> concentrated in the center of
> the population.  That's why we have Proportional Repsentation.
>
> Also the purpose of stochastic single winner methods ("lotteries") is to
> spread the probability around to
> avoid the tyranny of the majority.
>
> But if we want a deterministic single winner method, then we want the
> winner to be as representative of
> the population as possible, i.e. as close to the "center" of the population
> as possible.
>
> Of course there are many possible definitions of "center."  But in the
> centrally symmetric distributions
> used in Yee diagrams all of these definitions coincide.  So if Yee diagrams
> of the method fail to yield
> Voronoi polygons, the method is not centrist enough.
>
> Have Badinski and Laraki subjected their method to Yee analysis?
>

No, and it would not be trivial to do so; it would involve making some
assumption about what distance to rating function voters used. I'm sure
they'd argue for an absolute function, which would result in many ballots
not spanning the full range of ratings; unlike with Range, this is not
necessarily unstrategic. This would, if my intuition serves me, result in
somewhat-fuzzy Voronoi diagrams. But if you scaled all votes to cover the
full range of ratings, I suspect you'd get some non-voronoi, non-fuzz
artifacts.


>
> I know it's boring for all of the politicians to posture as centrists; no
> matter where the polls tell them that
> it is, they will lie just as freely as they always have.  The task of the
> voter is still the same: to discern
> who is telling the worst lies, and who has been bought off by which
> interests the most.


> The only case in which Badinski and Laraki have a leg to stand on is the
> case of a bi-modal distribution
> of voters with two prominent humps.  If that is a permanent feature of the
> electorate, then it is important
> to replace the single winner institution with a more representative
> multi-winner one, or to use a lottery
> method.  Think of the Hutus and Tutsis of Rwanda.
>

I disagree. There are some dynamics which Yee diagrams and the like do not
capture. Some candidates are simply better than others. I support a
deterministic method which has fuzzier Yee diagrams (up to a point), because
that makes it more sensitive to such considerations.


>
> It seems to me that in most cases it is more likely that the double hump is
> an artifact of the divisiveness
> of a method that doesn't elect centrists.
>

To a large extent, yes; but I would also argue that partisan media such as
Fox can create their own hump, and that this effect is independent of voting
system.

JQ

ps. Actually it turns out that it's Balinski, not Badinski. My mistake.
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