[EM] RE: clone winner and three slot ballots

[Simmons, Forest]

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Mike asked: Is Clone-Winner the same as the Independence from Clones Criterion (ICC)?
 
I reply: I understood it to mean that if a winner is cloned, then the winner must come from the new clone set.

I intended the votes-only version of this in my posting.
 
Mike went on to say:

The disadvantage of defining ICC in terms of votes-only is that Approval and
Purality pass, which is contrary to what people intend with ICC. There are
ways that are used, with some votes-only criteria, to keep Plurality from
winning, but they're all pretty undesirable, as I've been discussing on EM.
Preference ICC is universally and uniformly applicable, and it makes no
mention of methods' rules, including their balloting rules. That can't be
said of the votes-only versions.

I reply: I agree that the preference version is better than the votes-only version, but also believe that votes-only is better than nothing.  In particular, I think that the votes-only version is adequate in the case of Approval.
 
Mike goes on to pose an example:

Anyway, say your preference ordering is: A>B>C. And say that {A,B} is a
clone-set. One way to vote sincerely would be to vote 1A, 2B.
 
[which is the same as A>B>C in the three slot context]

Say B wins, by one vote, in the Approval phase of MDDA3.

Now we add C to the election. Say you like C better than A and B. Now, your
only sincere ballot is:
C>A>B. 
 
I interrupt:  I presume that this new C is different from the one in the first paragraph of your example where you wrote A>B>C.
 
So let's call this new candidate C'. 
 
So far we have the preference order for the voter as  C'>A>B>C.
 
If this C' is a clone of previous winner B, then since A is ranked between C' and B, the candidate A must also be in the clone set.
 
Since there are only three slots on the ballot, and the only non-clone C must not be mixed in with the clones, the only clone consistent way to modify the ballot from A>B>C is to change it to
 
C'=A>B>C  or  to  C'>A=B>C .
 
In either case the clone set occupies only two slots on the ballot.
 
Under MDDA the new winner must come from this clone set {A,B,C'}.
 
Forest
 
 
 
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