[EM] Condorcet Meeting: Narrowing the Field

[Forest Simmons]

Say the finalists are the IRV winner together with any and all of its
"enemies" (defined as those candidates that defeat it pairwise).

If the IRV winner has no enemies, no need for any further runoff beyond the
Instant Runoff that just popped out the IRV winner.

If the IRV winner has precisely one enemy, then the two-candidate final
runoff will be a no stress sincere choice for the voters.

Otherwise, you have a potentially interesting runoff with "around 3 to 5
candidates" to put the Condorcet Meetng through its paces.

fws

On Thu, Aug 31, 2023, 11:51 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> Could the Implicit Approval winner ever be a Condorcet loser?
>
> Highly unlikely, especially in the context of too many candidates, etc.
> But if so, every other candidate would have a short beatpath to it ... so
> no narrowing of the field would occur.
>
> So it would be better to use the IRV winner or the MaxMax Pairwise Support
> winner as the short beatpath target ... the winner of the simplest method
> that satisfies the Condorcet Loser Criterion.
>
> On Wed, Aug 30, 2023, 11:30 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Voters strictly rank as many candidates as they care to.
>>
>> The implicit it approval of a candidate is the number of ballots on which
>> it out ranks at least one other candidate.
>>
>> Let S be the set of candidates tied for most implicit approval.
>>
>> A candidate will advance to the final ballot if and only if it has a
>> beatpath of two or fewer steps to some member of S.
>>
>> fws
>>
>>
>>
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