Chris Benham chrisbenham-at-bigpond.com |EMlist| wrote:
I also wrote: Another criterion that applies to rankings/approval methods interests me, which I might call "Disapproval Later-no-Harm":
"Ranking a disapproved candidate must never harm an approved candidate".
Unfortunately, I don't think that can be guaranteed without violating the Condorcet Criterion (as Ted points out below). Any time you rank another candidate, you take a chance of making that candidate the CW and taking the win away from one of your higher-ranked candidates -- no matter how far down you rank the new candidate. Anyone who insists on LNH must give up on CC, I think (Please correct me if I am wrong about that).
I think it is safe to say that ranking another candidate is *less likely* to harm an approved candidate if the newly ranked candidate is disapproved rather than approved. How much less likely? That is a more difficult question!
In other words, the approval cutoff of DMC/RAV is not as strong as truncation, but it achieves a similar effect. It doesn't guarantee LNH but it helps, without violating the CC.
--Russ
(A stronger version would add "or a higher-ranked disapproved candidate"). This is incompatible with Condorcet, and in a future post I'll suggest a method that meets it.
Ted: "This goes around and around ... If you have such a method, I don't think it will satisfy the Condorcet Criterion.
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