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the method will probably get rescinded.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@gmail.com a écrit :

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@yahoo.fr wrote:

Hi Forest,

Le lundi 13 mars 2023 à 14:00:46 UTC−5, Forest Simmons forest.simmons21@gmail.com a écrit :

This is basically what I do measure now, which I would call the "face value" burial
incentive. If you insist on Condorcet and minimize this metric, it will lead you to
Schwartz//IRV, or I guess a method of the sort that Kristofer looks for. And you won't want
to use anything MinMax-like where you get to consider all the pairwise contests.

However, I think it's possible to arrange things so that successful burial depends on
getting lower preference support from voters who aren't that likely to be offering it. This
is based on the theory that voters will naturally end their ranking somewhere between two
frontrunners. So what I was thinking about is whether there could be a metric that
represents this idea.

Essentially you would concede that for some method, given totally random ballots, the
burial incentive looks horrendous. But after accounting for expected voter behavior, burial
mostly seems dangerous.

That I'm not sure.

Kevin
votingmethods.net

Kevin,

I'm thinking about my initial reaction towards Yee diagrams ... too ideal
... too simple .... how could we learn anything from it?

But I was pleasantly surprised!

Of course Yee is not what we're looking for ... but is there something else
simple and tame like Yee that might reveal some insights?

For example ...  distributions generated geometrically by n<10 random
points in the Cartesian plane ... each point is a candidate position and
each candidate has only one faction ... with all of its weight at the
candidate position.

Start with n=3, to confirm what we already think we know. Then increase n
gradually and methodically.

Along the way experiment with candidate withdrawal  to see what happens
when you have more factions than candidates, etc.

Start with all factions equal in size ... how often do you get a CW?

If that's too ideal to learn from or plagued with too many ties ... add
random small perturbations in faction size, etc.

Eventually replace some candidates with clone sets.

Or perhaps there is some other totally different simple approach.

Personally I would shy away from continuous or large finite distributions
or many factions for the same candidate (except those arising naturally by
candidate withdrawal) until getting a thorough grasp of the simple cases.

You probably already did all of this!

-Forest

On Wed, Mar 15, 2023, 10:04 PM Kevin Venzke stepjak@yahoo.fr wrote: