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

[Kristofer Munsterhjelm]

fsimmons at pcc.edu wrote:

> 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.

I think you said that these are related, even: that PR methods and 
stochastic single-winner methods are similar, seeking proportionality 
(the former in seats, the latter in time).

> 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 don't think they have, but if JQ is right in that it is similar to 
Bucklin, then presumably the Yee diagram would look similar to that for 
Bucklin (and median ratings). Neither of those two methods give the 
Voronoi-type Yee diagrams that Condorcet does.

> 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.

In a less divisive single-winner method (with respect to Plurality) like 
Condorcet, the centrist could still win. If the voter preference 
distribution is made out of two Gaussians, then while nobody 
particularly likes the centrist candidate/s between the two peaks, it 
may be better to both Hutus and Tutsis (as it were) than getting killed 
by a zealous candidate at the other peak.

There may also be another scenario where Majority Judgement (or median 
ratings, for that matter) would do better than ranked methods. If it's 
possible for the voters to agree on what, say, "Good" means 
(comparability of utilities), then MJ might extract usable cardinal 
information from the voters, while the strategy resistance makes the 
cardinal information much less prone to the sort of Approval-reduction 
that you would see in Range. If one holds certain assumptions that make 
cardinal methods useful at all, then MJ could well be strategy resistant 
enough that it would do better than Range*.

B&L spends quite a bit of their paper on the claim that the voters *do* 
agree on what the different categories mean, and so that there is 
comparability so that the cardinal information can be used.

* You could even consider majority compliance a DSV property. Say some 
method X doesn't satisfy majority. Unless it's supermajority based, it's 
reasonable to assume that a strategic majority could force the winner of 
method X. Making a method derived from X automatically satisfy majority 
just takes this strategy out of the hands of the voters, so that they 
don't have to strategize.