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

[Jameson Quinn]

2011/7/13 Kristofer Munsterhjelm <km_elmet at lavabit.com>

> 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.


Yee himself gives Voronoi diagrams as "approval" results, using a
probabilistic absolute cutoff, I think with a logarithmic distribution. In
fact, absolute and not relative ratings are much more sensible with MJ than
with Approval, and I haven't actually done the simulation, but I'm pretty
sure that they would give Voronoi diagrams as well, though they would be
fuzzier at the edges than Approval's.

Using relative ratings, as you say, the system would end up looking more
like Bucklin.

>
>
>  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.
>
>
Yes. MJ is not majority compliant for preferences - a candidate can be
preferred by a majority and still lose - but it is majority compliant for
ratings - if a majority rates candidate X at or above some rating and all
others below, X will win. So the comparability of cardinal information is
key to the method. B+L insist on this comparability not just using
theoretical arguments, but empirically; for instance in the 2007 French
election they polled, "everyone with an awareness of French politics who saw
anonymized results" was thus able to name all four major candidates, even
though the ordering differed from the final official results. This is
something I highly doubt would be true for a purely ranking system.


> * 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.
>
> Yes.

JQ
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