[EM] Burial and Defection with the "defeat-droppers".

[Chris Benham]

James G-A,
In this excellent  burial/defection example of yours:

46 abc
44 bca (sincere is bac)
05 cab
05 cba

A is the sincere CW and also the sincere (and voted)
FPP and IRV winner,and yet all the "defeat-dropping"
Condorcet methods (plus SCRIRVE) elect the Buriers'
favourite, B.  I consider this example to be much more
serious and horrific than any 3-candidate example that
I've ever seen used to attempt to discredit IRV or 
DD(Margins).Of this, you wrote (Mon.Mar.14):

 "This is a hideous result that would shower Condorcet
methods in shame for generations to come."



So the obvious question I ask you is this:  Why then
do you reccomend methods that  elect B?
Or to put it another way: What in your opinion is so
bad about the methods that don't elect B?

"Like what?" you may ask.  Before getting into that,
I've a couple of questions relating to the above
election:
(1)Do you (or anyone) know of any method that doesn't
elect B and also meets (mutual)Majority, Clone
Independence and Mono-raise (monotonicity)?

(2)Do you (or anyone) know of any method that doesn't
elect B and also meets  Minimal Defense and the
Plurality criterion?


I've cast "not vulnerable to Burying"  into a formal
criterion/property:

" Burial Resistance: If candidate x wins, and
afterwards some ballots that rank any y above x and 
any z are changed so that z's ranking relative to x is
raised while keeping y ranked above both; then if
there is a new winner it cannot be y."

Unfortunately that is a very strong criterion, and the
only methods that I can think of that meet it are IRV
and FPP. So how to weaken it so as to usefully
distinguish some Condorcet methods from others?  With
the above scenario in mind I've come up with two
"weakenings".

"Weak Defection Resistance: If  winning candidate x is
the CW and the FPW, and xy are a solid coalition with
more than 2/3 of the votes; and afterwards  some
ballots that rank y above x and z are changed so that
z's ranking relative to x is raised while keeping y
ranked above both; then if there is a new winner it
cannot be y."

"Weak Burial Resistance: If winning candidate x is the
CW and FPW while z is the CL and FPL , and afterwards 
some ballots that rank any y above x and z are changed
so that z's ranking relative to x is raised while
keeping y ranked above them both; then if  there is a
new winner it cannot be y."

"Weak Defection Resistance" (WDR) is the
Burial-related criterion I referred to in my last
message. It is met by Raynaud (GL).
I'll give some more method ideas in a later post.

Chris Benham








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