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

[Forest Simmons]

Here's another hint.

Which of the listed methods elect the approval winner A for the following
ballot profile?

46 A
5  A=C
5  B=C
44 B

On Wed, Dec 7, 2022, 4:43 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20221208/19c63d6c/attachment.htm>