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

[fsimmons at pcc.edu]

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

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?

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.

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.

----- Original Message -----
from: Jameson Quinn 
> 2011/7/11 
> 
> > Yes, by sequentially eliminating one member of the remaining largest
> > diameter pair, the method elects a
> > centrist.
> >
> > If this is considered a problem, it can be overcome by sequentially
> > eliminating one member of the
> > current smallest diameter pair. However, this variant 
> introduces a strong
> > incentive for compromise,
> > which is nil in the other version.
> >
> 
> The point which Badinski and Laraki advocate is that neither all-
> centristsnor all-extremists is good. I think that this second 
> proposal is at least as
> subject to center-squeeze as IRV, if not more, so like IRV it 
> would class as
> "too extremist" by their reckoning.
> 
> JQ
> 
> 
> >
> > ----- Original Message -----
> > From: Jameson Quinn
> > > This system seems explicitly designed to elect a centrist. 
> In their
> > > experimental
> > > paperonMajority Judgment, system inventors Badinski and 
> Laraki run a
> > > simulation
> > > to see how often different systems elect a centrist. Most
> > > systems they test
> > > either elect the centrist almost always (ie, condorcet systems)
> > > or almost
> > > never (plurality, IRV, runoffs), but their MJ system does about
> > > half the
> > > time. They argue that this "lack of bias" either towards or 
> away from
> > > centrists is best, because a system which is too skewed to the
> > > middle or to
> > > the extremes will distort the political dialogue in
> > > corresponding ways.
> > > Though I think their simulation is just a rudimentary first
> > > step, I find
> > > their normative argument convincing; and so I don't really 
> like this
> > > "distance" method.
> > >
> > > JQ
> > >
> > > 2011/7/10
> > >
> > > > First find a clone consistent way of defining distance between
> > > candidates.>
> > > > Then while two or more candidates remain
> > > > of the two with the greatest distance from each other
> > > > eliminate the one with the greatest pairwise defeat
> > > > EndWhile.
> > > >
> > > > Various variants are possble. For example, you could count
> > > defeats only
> > > > from the remaining
> > > > candidates. Also there are various possible measures of
> > > defeat strength.
> > > > In that regard, if you say that
> > > > any defeat by covering is stronger than every non-covering
> > > defeat, then the
> > > > method will always elect a
> > > > covered candidate.
> > > >
> > > > To get a distance estimate in a large election you could just
> > > ask each
> > > > voter to list the pair of candidates
> > > > that seem the most different on the issue or combination of
> > > issues of most
> > > > concern (to that voter). The
> > > > pair submitted by the greatest number of voters would be the
> > > first pair
> > > > considered, etc.
> > > >
> > > > What potential for manipulation does this direct approach 
> introduce?> > >
> > > > Perhaps voters would try to pit their favorites' rivals
> > > against each other.
> > > > Would that be insincere? Not if
> > > > they consider their favorite to have a reasonable middle of
> > > the road
> > > > position, while viewing the rivals as
> > > > being at opposite unreasonable extremes.
> > > >
> > > > What indirect measure of distance could be used?
> > > >
> > > > If we count the number of ballots on which candidates X 
> and Y
> > > are ranked at
> > > > opposite extremes (top
> > > > rank for one versus unranked for the other), the monotonicity
> > > of the method
> > > > would probably be
> > > > destroyed. Is there a more subtle way of inferring the
> > > distance that
> > > > wouldn't destroy the monotonicity?
> > > >
> > > > ----
> > > > Election-Methods mailing list - see http://electorama.com/em
> > > for list info
> > > >
> > >
> >
>