[EM] Re: Burying and defection with the "defeat-droppers".

[James Green-Armytage]

Hi Chris,
	Some replies follow...

>46 abc
>44 bca (sincere is bac)
>05 cab
>05 cba
>
>So the obvious question I ask you is this:  Why then
>do you reccomend
>methods that  elect B?

	Do I? First of all, my recommendation of winning votes methods is
tenuous. Second, I suggest that this would be an unrealistic winning votes
example, because I expect that in a real wv election of this type, most of
the A>B>C voters would truncate before B, and most of the B voters would
truncate before A.
	My primary single-winner recommendation is cardinal pairwise (CWP). I
find it highly unlikely that CWP would pick any candidate other than A in
this example.
>
>Do you (or anyone) know of any method that doesn't
>elect B and also
>meets (mutual)Majority, Clone Independence and
>Mono-raise (monotonicity)?

	Cardinal pairwise meets mutual majority and monotonicity. It doesn't meet
clone independence in its traditional form, but it does meet an alternate
(ratings-adapted) version of the criterion that requires clones to be
given equal ratings. Anyway, the clone failure is very minor compared to
minimax or Borda.
>
>Do you (or anyone) know of any method that doesn't
>elect B and also
>meets  Minimal Defense and  the Plurality criterion?

	I don't know if CWP meets these. Criteria that are designed only for
ordinal information are not always friendly to CWP.
>
	I haven't looked into criterion compliance of other anti-strategy methods
such as AWP, S/WPO, AERLO/ATLO, etc. You're welcome to do so.
>
>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. 

	Right... I think we established awhile ago that Condorcet-efficient
methods will always be somewhat vulnerable to the burying strategy.

>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, 

what's this? plurality winner?

>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."

	Does anything interesting meet this criterion?
>
>"Weak Defection Resistance" (WDR) is the
>Burial-related criterion I
>referred to in my last message. It is met by Raynaud
>(GL).

	A proof?

my best,
James