[EM] Burial Detection & Correction

[Forest Simmons]

Kevin,

Here's what I had in mind:

1.Generate a random ballot profile.

2. If it has either a majority faction or a Condorcet cycle, discard it.

3. If there is a unilateral order reversal that creates a cycle, do one at
random, and check to see which Condorcet completion methods reward the
reversal.

increment the counters of success and failure.

4. Repeat ...

Am I being too naïve ?

How much difference would it make to generate the profiles geometrically?
Would it be worth the extra trouble?

Thanks!

Forest

On Sun, Mar 12, 2023, 10:20 AM Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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
>
>
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