<div dir="auto">Oh, hmm, that sounds like Split-Cycle maybe?</div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Apr 22, 2024 at 1:16 PM Joshua Boehme <<a href="mailto:joshua.p.boehme@gmail.com">joshua.p.boehme@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><br>
A graph theorist would call it a Hamiltonian path over the tournament graph (provided that pairwise ties are drawn as edges in both directions instead of the usual no-edge convention). That isn't standard terminology when talking about voting methods, though.<br>
<br>
<br>
One nice thing about Hamiltonian-path/beat-chain methods -- which also include Ranked Pairs and Kemeny-Young -- is that they automatically satisfy Smith. Moreover, they do so successively: first come all Smith set members, then the members of the Smith set over the remaining candidates, then...<br>
<br>
<br>
<br>
On 4/22/24 07:59, Chris Benham wrote:<br>
> A question I forgot to answer:<br>
> <br>
>> It makes sense to start with Approval-ordering & then adjust to fix the most important pairwise contradictions by switching. But aren’t the * biggest* margins more important than the smallest ones? Then why fix the smallest-margin mis-orderings first?<br>
> <br>
> Our aim it produce a "beat chain" (if that's the right term) where every candidate beats the next-lowest in the order down to the bottom, which is most in harmony with the approval order. No out-of-order pair of adjacent candidates is going to be left out of order.<br>
----<br>
Election-Methods mailing list - see <a href="https://electorama.com/em" rel="noreferrer" target="_blank">https://electorama.com/em</a> for list info<br>
</blockquote></div></div>