[EM] clone-immunity - definition please?

[Abd ul-Rahman Lomax]

At 08:06 PM 1/26/2007, Warren Smith wrote:
>If we have voting methods that input rank orderings WITH EQUALITIES permitted,
>then it is not clear to me what immunity to cloning should even mean, exactly.
>Throw in nondeterminism such as random tiebreaking, and it gets murkier still.
>
>Does anybody have a nice definition that does not contradict itself 
>in short order?

Fools rush in where angels fear to tread.

What is the problem with the definition of clone? There seem to be 
two definitions, if I look at Wikipedia. One is that the two 
candidates are identical. This would require equal rating in Range, 
for example, and Range would clearly pass ICC. The other is that the 
candidates are only ranked identically, which allows some difference 
in rating in Range, and some differences in rating could shift the 
outcome, without disturbing the ranking.

But in Range, if we neglect normalization (the process by which a 
voter may shift ratings in order to generate at least one vote at the 
extremes), then the rating of each candidate is theoretically 
independent of the rating of every other candidate. You do not raise 
one by lowering another, and vice-versa. So inserting or removing a 
clone should have no effect.

Because of normalization, inserting a new max low candidate, or max 
high, could affect the ratings of other candidates, but not if voters 
magnify. In this case a new max low candidate would simply be rated 
zero together with the previous max low candidate, or 100% together 
with the previous max candidate.

But this effect would not happen with exact clones. With rank-order 
clones, though, inserted at the top for a voter, a clone who is rated 
a little higher than the original winner by a voter might lower the 
rating, perhaps by one click, of the previous high rated candidate. 
This loss of a click could cause that candidate to lose.

But it is problematic to allow voters to change their ratings in 
considering ICC. It is artificial to confine clone to "rank-order 
clone" when we are considering a method which considers more than 
rank order. Indeed, it should not be surprising that criteria that 
apply specifically to ranked methods, but which do not consider 
preference strength, could fail Range. Starting with the Majority 
Criterion, as some define it, and the Condorcet Criterion. ICC would 
be no different. If you assume that rank order is all there is in 
designing a criterion, something that takes an additional factor into 
consideration *must* under some circumstances alter the outcome, or 
else why bother collecting the additional data?