[EM] IRV's Squeeze Feature

[Chris Benham]

Forest,
You wrote, setting up your attack on IRV:
"Suppose that the voters are distributed uniformly on a disc with center C, and that they are voting to 
choose from among several locations for a community center."

(a) That is quite a big "suppose", and  (b) I agree that IRV would not be among the best methods
to use to vote to choose the location of a community centre.

"The center C of any distribution of voters with central symmetry through C will be a Universal Condorcet 
Option for that distribution."

Yes, that is almost a tautology (and to the extent that it isn't it seems to be just a semantic point).

"And what justification for winning does the IRV winner have?"

I agree that if we suddenly have unfettered access to all the voters' sincere pairwise preferences and that
each voter's different pairwise preferences are all at least approximately as strong as each other, then yes
electing the Condorcet winner is "nicer" and philosophically "more justified" than electing the IRV winner. 

However the IRV winner could have as its justification simply the criterion compliances of the IRV method.
You, as the "election-method salesman", could say to the polity/voters  'customer':
"This Condorcet method is definitely best for choosing the most central community centre with sincere voting. 
I recommend it." 

but they could reply: 
"Does it meet Burial Invulnerability and Later-no-Harm and Later-no-Help as well as Mutual Dominant Third 
and Mutual Majority and  Condorcet Loser and Woodall's Plurality criterion and Clone Independence?"

To which you must reply "No", and then the 'customer' says "Then which is the best method that does?", to
which you reply "IRV" and make the sale.

IRV has some more-or-less unique problems but they are the unavoidable price of  a unique set of  strengths,
so I don't consider it justified to focus on its problems in isolation. Often this is done, comparing (sometimes
implicitly) IRV with the best features of several other methods. 

But as you know, I am also supportively interested in Condorcet methods and also Favourite Betrayal 
complying methods such as 3-slot SDC,TR.

Chris Benham



Forest Simmons wrote (Fri. Dec.5):
Suppose that the voters are distributed uniformly on a disc with center C, and that they are voting to 
choose from among several locations for a community center.

Then no matter how many locations on the ballot, if the voters rank them from nearest to furthest, the 
location nearest to C will be the Condorcet Option.

Therefore, if C itself is one of the options, it will be the Condorcet Option no matter what the other 
options are.  So C is more than just a regular run of the mill Condorcet Option, it is a kind of Universal 
Condorcet Option for this distribution of voters.

The center C of any distribution of voters with central symmetry through C will be a Universal Condorcet 
Option for that distribution.

But no matter how peaked that distribution might be (even like the roof of a Japanese pagoda) the center 
C is not immune from the old IRV squeeze play.

If the good and bad cop team gangs up on C, one on each side, they can reduce C's first choice region 
to a narrow band perpendicular to the line connecting the two team mates, thus forcing C out in the first 
round of the runoff.

If the team mates are not perfectly coordinated, then instead of a narrow band, C's first choice region 
becomes a long narrow pie piece shaped wedge, roughly perpendicular to the line determined by the two 
team mates.

This squeeze play can be used against any candidate no matter the shape of the distribution, symmetric 
or not.  But my point is that even in a sharply peaked unimodal symetrical distribution, the center C, 
which is the Universal Condorcet Option, can easily be squeezed out under IRV.  And what justification 
for winning does the IRV winner have?  Merely that it was the closer of the two team mates to the ideal 
location C.

Now leaving the concrete setting of voting for a physical location for a community center, and getting 
back to a more abstract political issue space: It doesn't really matter if the good cop and bad cop are 
really even anywhere near to opposite sides of a targeted candidate (say a strong third party challenger) 
as long as they can make it appear that way.

The two corporate parties are very good at this good cop / bad cop game, especially since the major 
media manipulators of public opinion are completely beholden to the giant corporations.


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