[EM] Burial Detection & Correction

[Kevin Venzke]

Hi Forest,

Not sure if I totally follow but the topic did have me thinking about the measurement of
the backfire rate of burial strategy. In simulations I normally assess the ability of
burial to work, without considering any threat of defensive strategy (presumably done via
truncation). I also measure minimal defense aka SDSC, which is sort of related, ensuring
that in at least one situation, burial "won't work." But we don't know how often that means
it does nothing, or backfires.

I'm trying to think of a new metric something like this: Suppose A is elected. Suppose no
A>B (relative order) voters rank B over anyone. Now some B>A voters attempt to bury A. Now
ask how often is the result that A still wins, vs. B now wins, vs. another candidate now
wins. (Interestingly, even an MD method could let B win sometimes, as MD is only a
guarantee for a full majority. It probably depends on what the method is doing to achieve
MD.)

The logic here is that if A initially won, then supporters of A might know that A was a
viable candidate, and that they could leave off any support for some other candidate
perhaps specifically in order to thwart a burial effort against A. The question of whether
A voters would reasonably do that is dodged, by only looking at scenarios where the A
voters observably *are* doing this and A is, of course, winning. (It's possible A had not
been winning before the hypothetical truncation on their part, and that's actually
necessary because the "before" case includes any scenarios where a burial strategy against
A succeeds through taking advantage of A voters' lower rankings.)

A considerable obstacle in measurement is that a scenario could have multiple possible
candidates "B" and there could be multiple ways to specify the ballots of burying voters
and multiple ways to select which voters those will be.

Another question is, what does "good" performance here look like? Of course, we don't want
burial to succeed. But do we definitely want it to backfire? If it backfires "often," then
in theory people won't want to do it. That's a little speculative. It might depend on the
method or situation. In real use, we need to not see backfiring burial strategies, or else
the method will probably get rescinded. Either backfiring must be impossible under the
method, or else burial must be too clearly foolish to try.

If the desirability of a high (theoretical) backfire rate has to be assessed on a case by
case basis, then we would probably need yet another metric to be able to interpret the first
one.

Kevin
votingmethods.net

Le samedi 11 mars 2023 à 15:52:20 UTC−6, Forest Simmons <forest.simmons21 at gmail.com> a écrit :
> Elect the pairwise undefeated candidate if there is one ...
> 
> Else let P be the covering pair with the strongest defeat strength (gauged by Winning Votes
> minus Losing Max Pairwise Support).
> 
> Elect the winner of a sincere runoff between the two members of P.
> 
> For this sincere runoff all you need is a fresh set of ballots dedicated exclusively to this
> runoff.
> 
> Oh ... and in the practically impossible event of non existence of a covering pair, elect
> the MiaxMinPS candidate ... the candidate whose Min Pairwise Support (on the original
> ballots) was maximal.
> 
> This method is intended for the Society of Game Theoretic Quantuum Computing Signal
> Processing Engineers ... should such a society ever be convened!
> 
> -Forest