[EM] ICC dfn I posted applies to Approval. Approval fails it.

[Michael Ossipoff]

It’s just occurred to me that, by the definition I’ve just posted, in an 
Approval election, every subset of the candidates is a clone set, because 
it’s impossible to vote a candidate between any two others in Approval.

So the ICC definition that I’ve just posted doesn’t apply to Approval. 
Approval neither passes nor fails that criterion, as I’ve just posted it. 
It’s only for comparing rank methods or RV with more than 2 rating values.

So, simplification could be gained by replacing the verb “vote” with “rank 
or rate”, in that ICC definition.

I’m not sure if the ICC definition that I’ve just posted is the one that we 
agreed  on  in discussion about it. It seems to me that we had a 
non-preference ICC definition that  applied to Approval, and which Approval 
failed.

Well, we had a longer definition of a clone-set:. It might have been this:

Everyone who votes a member of S over some candidate X votes every member of 
S over X; and if everyone who votes some candidate X over a member of S 
votes X over every  member of S; and if everyone who votes a member of S 
equal to some candidate X outside of S votes every member of S equal to X.

Having just written this, I don’t know if it would treat Approval 
differently than the definition in my previous posting.

But I suppose that that ICC definition in my previous posting could be  
applied to Approval. The deletion of a candidate shouldn’t change the matter 
of whether the winner comes from any subset to which that candidate belongs. 
Say X wins and we delete X.  There are subsets of the candidates that 
contain only X and candidates who lose in the subsequent count.  So Approval 
apparently would fail that ICC. So that ICC definition that I posted in my 
posting before this one _does_ treat Approval as one would expect ICC to 
treat Approval

Mike Ossipoff