[EM] Approval splitting pathology

[Etjon Basha]

A couple quick thoughts on this.


I see two risk factors to the vote split eventuating.


The first is how lenient one is in setting the approval cutoff within the
Smith Set in general: on one end, you approve of all members except the
least favorite (least risk) and on the other you approve of the top member
only (most risk).


The second is whether, in your scenarios, the original set of ballots that
elected A had A as the CW or as a member of Smith Set to begin with. If the
later, A’s clones will likely cluster higher within the Set from the pov of
the voter compared to the other, non-A Set members, so will be likely all
approved (but again, depends on the first factor above). If A was the CW
though and was the last candidate still approved off originally, at least
some of the clones won’t be approved by various voters, hence splitting.


Depending on how these two factors interact, you could get vote splitting
in such scenarios(?).


Or maybe this is entirely off the mark.



Regards,


Etjon

On Tue, Oct 22, 2024 at 9:32 AM Ted Stern <dodecatheon at gmail.com> wrote:

> As a long time fan of Margin Sorted Approval (AKA Approval Sorted Margins
> <https://electowiki.org/wiki/Approval_Sorted_Margins>), I've been
> thinking about various ways to improve it.
>
> I started thinking about how one might implement an automatic approval
> cutoff, designed to give each ballot its own strategically optimal cutoff.
>
> One reasonable strategy in Approval Voting generally is to determine, for
> each ballot, the highest ranked candidate(s) who are in the Smith Set, and
> then put the Approval Cutoff below that rank.
>
> But what happens if there is a Condorcet cycle, and the candidate who
> would ordinarily win in Approval voting ("A") using that strategy is cloned
> ("A1, A2, A3"). and there is a cycle in that clone set? With the
> strategy.above, the approval cutoff will be placed just below the top clone
> on the ballot. This would cause a split of approval for the A# candidates,
> affecting not only Margin Sorted Approval but also Approval Voting more
> generally.
>
> This special case seems highly unlikely, but it points to a cloning
> resistance issue with any Approval augmented Condorcet method.
>
> Thoughts?
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