[EM] Re: ICC and Approval

[MIKE OSSIPOFF]

James:

You said:

	So, ICC definition is changed to this, for use in evaluating non-ranked
methods:

I comment:

I trust that you meant "in evaluating both rank and non-rank methods". The 
kind of ICC that you describe applies meaningfully and usefully to rank 
methods and non-rank methods. To all methods.

I trust that you wouldn't use different ICC definitions, one for rank 
methods and one for non-rank methods.

You continued:

1. Clones: A set of candidates such that for every candidate outside the
set, all voters either prefer the outside candidate to all inside
candidates, or prefer all inside candidates to the outside candidate.

I comment:

That wording could have more than one meaning. It could mean that either the 
candidate outside is unanimously preferred to all inside candidates, or all 
inside candidates are unanimously preferred to the outside candidate. That's 
one of the two meanings that definition could have, and it isn't the one 
that you intended.

That's the risk when you shorten a wording. Better to leave it long, 
awkward, and unambiguous.

One other thing: You left out the possibility that anyone who considers an 
inside candidate equal to the outside candidate considers all inside 
candidates indifferent to the outside candidate.

So here's how I'd say that:

Set S is a clone set if, for every particular voter, and for any candidate X 
outside S,  if that voter prefers somone in S to X than s/he prefers 
everyone in S to X; and if that voter prefers X to someone in S, then s/he 
prefers X to everyone in S; and if that voter is indifferent between X and 
some candidate in S, then s/he is indifferent between X and every candidate 
in S.

A voter is indifferent between X and Y if s/he doesn't prefer X to Y and 
doesn't prefer Y to X.

[end of clone-set definition]

A clone set, by that definition, can have as few as 1 member. In fact, of 
course, any set containing one candidate qualifies as a clone-set by that 
definition.

You continued:

2. Independence of clones: If a clone set has two or more members,
removing one of the clones should not have any bearing on whether the
winning candidate comes from the set. Likewise, adding a new clone to the
set should not have any bearing on whether the winning candidate comes
from the set.

I comment:

You left out the stipulation about how preference constrains voting. The 
usual one for ICC is that everyone votes sincerely.

A voter votes sincerely if s/he doesn't falsify a preference, or fail to 
vote a preference that the balloting system in use would have allowed 
him/her to vote in addition to the preferences that s/he actually did vote.

[end of sincere voting definition]

You continued:

	I have proposed a modified version of ICC such that candidates must be
given identical cardinal/approval scores by all voters to qualify as
clones, in addition to the standard qualification rule. I believe that
approval and cardinal pairwise both pass this modified version of ICC, but
not the standard ranked ballot version.

I comment:

No criterion should have a special ranked-ballot version. The ICC that you 
described, or my improved wording of it, is ICC for all methods.

Additionally, your alternative definition refers to Approval and CR ratings. 
It's unnecessary and undesirable for a criterion definition to mention 
methods, balloting rules or other method rules.

By your alternative clone-set definition, there can be no such thing as a 
clone-set with more than one candidate when the method is Plurality, or when 
the method is Borda or IRV, as those latter two are usually propoed. Some 
would say that that means that the criterion doesn't apply usefully to 
Plurality, IRV, or Borda. Some would say that Plurality, IRV, and Borda pass 
the criterion, but in a meaningless way, as a ham-sandwich would. It doesn't 
matter which of those positions you agree with. The important thing is that 
that criterion would be useless for comparing Plurality, Borda, or IRV to 
any other methods (including eachother).

One could write a preference clone set definition that says that S is a 
clone set if everyone is indifferent between S's members. Pluralty, Borda, 
and IRV would fail the resulting criterion, meaningfully. But you shouldn't 
call it a clone set, because that name is already taken. How about 
"indifference set"?

Then the resulting criterion could be called "Indepence from Indifferenent 
Candidates Criterion" (IICC)

IICC is a valid criterion (at first glance, at least). Maybe it's useful for 
comparing methods.

It's met by Approval and CR, and probably by MMPO and wv. So it looks like a 
good country-club to belong to.

Mike Ossipoff

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