[EM] "Margins Sorted Approval" poll candidate

[Joshua Boehme]

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.


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...



On 4/22/24 07:59, Chris Benham wrote:
> A question I forgot to answer:
> 
>> 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?
> 
> 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.