[EM] Which methods reduce to Approval when no ballot ranks any candidate lower than equal first?

[Forest Simmons]

Toby,

You are very close ... only one of these fails to elect the approval winner
when fed approval ballots.

I'm going to give everybody one more day to figure out which one, and what
about it makes the difference.

On Wed, Dec 7, 2022, 1:42 AM Toby Pereira <tdp201b at yahoo.co.uk> wrote:

> Presumably ranking top means the highest possible score in the cardinal
> methods. Intuitively it seems that pretty much all of these methods should
> elect the approval winner. The Condorcet ones surely. I'm not sure what
> justification there would be for not doing so, so it sounds like the birth
> of a new criterion.
>
> Toby
>
> On Wednesday, 7 December 2022 at 02:15:19 GMT, Forest Simmons <
> forest.simmons21 at gmail.com> wrote:
>
>
> Suppose that for some ballot B, the only candidates ranked on B are the
> ones ranked Top or Equal Top. In that case we say that B has been voted
> "approval style".
>
> Suppose that every ballot in the entire ballot set is voted approval
> style. Which of the following methods will elect the approval winner (the
> one voted Top or Equal Top on the most ballots)?
>
> Range/Score, Bucklin, Ranked Pairs, Copeland, Majority Judgment,
> Kemeny-Young, STAR, Approval Sorted Margins, DMC, IRV, DAC, DSC, MMPO,
> River, Schulze CSSD, Baldwin, Nanson, Black, MinMax(margins), SPE, Gross
> Loser Elimination, BTR-IRV, Score Chain Climbing, List Based Banks, Benham?
>
> I won't give away the answers until tomorrow ... so you can think about it.
>
> Then, after some additional questions to explore, a new method ... a
> natural outgrowth of our new understanding!
>
> -Forest
>
>
> 6
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