[EM] WMA (It's not monotonic or participation compliant, after all)

[Kevin Venzke]

Hi Forest,

--- En date de : Lun 3.5.10, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> De: fsimmons at pcc.edu <fsimmons at pcc.edu>
> Objet: [EM] WMA (It's not monotonic or participation compliant, after all)
> À: election-methods at lists.electorama.com
> Date: Lundi 3 mai 2010, 18h06
> Kevin and Chris,
> 
> You’re both right, my “proof” only showed that
> raising the winner W could not hurt her prospects on 
> ballots where she was already approved or on ballots where
> she was rated at the highest currently 
> unapproved level.  But , as Kevin pointed out, if
> there were candidates at two or more levels above W, 
> and not all of these levels were above the current cutoff,
> the cut off could lower without lowering all of the 
> way down to W.
> 
> Back to the drawing board.  I’m starting to think
> that it may be impossible to have any kind of 
> monotonic, non-trivial DSV method for automatically
> choosing approval cutoffs.

I definitely think it is impossible. If you let voters choose their
cutoff based on "X," it's impossible to guarantee anything about how you
are using "X." And "X" is probably affected by raising candidates.

I think you will have to greatly constrain how much "freedom" the voters
have to place the cutoff. It will have to be based on as little 
information as possible.

For instance you can view the situation in Bucklin as that voters lower
their threshold continually until the method ends. If you raise a winner
the method may just end sooner, but with the same outcome. Though for
a DSV method this leaves voters relatively quite "blind." They can't
"react to threats," they just gradually become impatient and start to
compromise.

I like my old (non-monotonic) "Conditional Approval" method where (if
we assume a three-slot ballot) voters repeatedly add in their second-slot
approval whenever the current leader is a disapproved candidate. No
one can retract second-slot approval once granted. The method ends with
the round where nothing else changes.

The justification for failing LNHarm feels more tangible than is often
the case: If we didn't count your lower preference (and those like it)
when we did, the winner would've been somebody that you said you didn't
like.

Kevin