# [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