[EM] A distance based method

[Jameson Quinn]

You can read the paper - I linked it - if you want to. Without going back
and quoting them, basically they argued that if a method always elects
centrists, candidates will always be competing to be the "most centrist",
which will make it difficult for voters to make a meaningful choice. They
also argue that if a method almost always elects extremists (as with
Plurality in their simulation), the political culture will become one of
extremism and polarization. I would argue that this latter effect is clearly
visible in US politics.

Note that their definition of "centrist" and "extremist" was based entirely
on a single election, the 2007 French presidential election. They ran 10K
simulations of variants of this same election, seeded by real polling data.
(You can also see a summary of their results on
wikipedia<http://en.wikipedia.org/wiki/Voting_systems#Experimental_criteria>.)
That's enough data to clearly show some differences between systems, but
it's not clear how robust those differences are under different conditions.

2011/7/11 Juho Laatu <juho4880 at yahoo.co.uk>

> Do you know remember their arguments, or your own, on why centrists are not
> good? I think methods that elect centrists (like CW) are quite good general
> purpose single-winner methods. But on the other hand there are many kind of
> single-winner elections, and in many cases the targets may well be very
> different.
>
> Some thoughts on why we might not recommend not always electing a
> "centrist" candidate:
> - we want to alternate between different parties, not to elect from the
> "centrist" party every time
> - we want to have proportional representation of all parties in time (based
> on lottery or credit votes)
> - we want to elect from major parties (not from _small_ centrist parties)
> - we want to have a system that exaggerates small changes in balance so
> that the policy will always reflect the current needs and tendencies
> (electing centrists may lead to having no changes in the policy and voters
> having no influence on the policy)
>
> We could also have different definitions of what "centrist" means. Maybe
> the second option below is the default value.
> - no extreme opinions in any questions (close to median opinion in all
> questions) (= "median opinions")
> - second preference of many voters, or typically in the first half of the
> individual rankings, close to being a Condorcet winner (= "good in pairwise
> comparisons")
> - accepted or ranked quite high by many voters in all parties / segments of
> the society (= "wide support")
>
> Juho
>
>
>
> On 11.7.2011, at 13.06, Jameson Quinn wrote:
>
> This system seems explicitly designed to elect a centrist. In their
> experimental paper<https://sites.google.com/site/ridalaraki/xfiles/BalinskiLarakiExperiEvid%28LastVersion%29.pdf?attredirects=0>on Majority 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 <fsimmons at pcc.edu>
>
>> 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?
>>
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