[EM] weak burial resistance criteria
James Green-Armytage
jarmyta at antioch-college.edu
Fri May 27 06:37:07 PDT 2005
Chris, you wrote:
>As far as I know, the only two significant measures of Burial
>resistance available are complete invulnerability (such as with IV and
>PP) and this one suggested by my criterion.
How do we measure vulnerability to burying? It's difficult! I don't think
that yes/no criteria alone are adequate for this purpose. It's a
qualitative judgement, and one that necessarily involves one's
understanding of voter behavior given conflicting incentives, uncertain
outcomes, partial information, etc.
You have defined a yes/no criterion aimed at evaluating burying
vulnerability. That's good, but other yes/no criteria are possible.
Here are a couple of weak burial resistance criteria for approval cutoff
methods.
(1) If C is the initial CW, and more than 1/2 of the voters approve C but
not Z, then the Z>C voters can't change the winner from C to Z.
(2) If C is the initial CW, and more than 1/3 of the voters approve C but
not Z, then Z>C voters can't change the winner from C to Z by creating a
false three-candidate cycle.
DMC, AM, and AWP pass (1). I believe that AWP passes (2), but that DMC
and AM do not.
Here are the corresponding weak burial resistance criteria for cardinal
methods. Assume that v is the number of ballots cast, and that the ballot
is a scale from 0 to r.
(3) If C is the initial CW, and the winning rating differential of the C>Z
defeat is >rv/2, then the Z>C voters can't change the winner from C to Z.
(4) If C is the initial CW, and the winning rating differential of the C>Z
defeat is >rv/3, then the Z>C voters can't change the winner from C to Z
by creating a false three-candidate cycle.
Cardinal pairwise passes (3) and (4). I'm not sure, but I think that a
"marginal rating differential" method would probably pass (3) but not (4).
Here is another weak burial resistance criterion for ordinal methods:
(5) If C is the initial CW, C has a majority-strength win over Z, and the
C>Z majority rank Z as tied for last, then the Z>C voters can't change the
winner from C to Z.
I believe that WV passes (5) but margins fails it. It is similar to SDSC
and minimal defense.
I expect that more criteria along similar lines are possible, in
addition to the ones that I have listed here. Do such criteria alone
enable us to make a definitive judgement on the relative burying
vulnerability of the different methods? No, not at all. Nevertheless, they
are somewhat helpful. Your own "weak burial resistance criterion" is
somewhat helpful as well. However, I think that it is one weak burial
resistance criterion among many, rather than the only significant one.
my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm
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