[EM] Re: "Approval Later-no-Harm",

[Russ Paielli]

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.