[EM] Burial Detection & Correction

[Forest Simmons]

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 at yahoo.fr> wrote:

> Hi Forest,
>
> Le lundi 13 mars 2023 à 14:00:46 UTC−5, Forest Simmons <
> forest.simmons21 at 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 ?
>
> 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.
>
> > How much difference would it make to generate the profiles
> geometrically? Would it be
> > worth the extra trouble?
>
> That I'm not sure.
>
> Kevin
> votingmethods.net
>
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