Clone Independence Criteria

[Norman Petry]

Dear Markus,

Thanks for bringing this difference in clone independence criteria to our
attention.  I had assumed that Tideman's "Independence of Clones" criterion
was the same as what we've been calling GITC ("Generalised Independence of
Twins Criterion"), and which you've redefined below as "Generalised
Independence of Clones Criterion".  I like the term "clones" better than
"twins", as twins implies only pairs of two (and there _are_
twin-independence
criteria which some methods satisfy, although they fail clone independence),
so I'd suggest we use the following shorthand nomenclature when referring to
these two variants in future:

"TICC" - Tideman's Independence of Clones Criterion (Tideman's definition)
"GICC" - Generalised Independence of Clones Criterion (Schulze's
definition).

Since any method which satisfies TICC also satisfies GICC, but not
vice-versa, GICC is obviously more useful in practice as a means of
differentiating voting methods.  One consequence of this difference in
definitions is that Tideman's method (even the improved form) is inferior to
Schulze's method in yet another respect -- Tideman's method probably doesn't
satisfy GICC (to say nothing of GMC!).

***

One of the problems I have with any of these clone-independence criteria is
that the situations they are designed to cope with are somewhat artificial.
While clone sets of a sort definitely exist in the real world (call them
"party members" or "factions"), they're "fuzzy", in the sense that there
usually won't be perfectly clean divisions between the sets in the minds of
all voters.  In most elections, there will be a few voters who don't vote
along party/faction lines (picking and choosing from multiple parties),
thereby destroying the perfect clone sets which are probably needed for
these criteria to work their magic.

So, in the real world, we're usually faced with the problem of near-clone
sets, rather than true clone sets.  The question is: does compliance with
GICC or TICC help to correctly resolve these types of problems?  Obviously
TICC compliance is certain to be less useful than GICC, since the possible
ballot configurations it allows are fewer than what GICC would permit, while
still identifying clone sets.  Still, I'd be interested to know if anyone's
done analysis on whether GICC is at least sometimes helpful with the
near-clone set problem.


Norm Petry


-----Original Message-----
From: Markus Schulze <schulze at sol.physik.tu-berlin.de>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Date: August 26, 1998 5:27 AM
Subject: Re: Random Ballot Tiebreaker



[...]
>
>Quoting Tideman, Norman wrote (25 Aug 1998):
>> "A proper subset of two or more candidates, S, is a set
>> of clones if no voter ranks any candidate outside of S
>> as either tied with any element of S or between any two
>> elements of S."
>
>To my opinion, Tideman's definition is too weak. I prefer
>the following definitions (3 Oct 1997):
>
>Definition ("clones"):
>
>   A[1],...,A[m] are a set of m clones if & only if
>
>   for each pair (A[i],A[j]) of two candidates
>   of the set of m clones,
>
>   for each voter V, and
>
>   for each candidate C outside the set of m clones
>
>   the following statements are valid:
>
>   V prefers A[i] to C, if & only if V prefers A[j] to C.
>   V prefers C to A[i], if & only if V prefers C to A[j].
>
>Definition ("Generalized Independence of Clones Criterion"):
>
>   A voting method meets the "Generalized Independence
>   of Clones Criterion" if & only if additional
>   clones cannot change the result of the elections.
>   [If one clone is elected instead of another clone of the
>   same set of clones, then this is not regarded as a change
>   of the result.]
>
>The aim of clone criteria is to verify, whether a method can
>be manipulated by presenting additional candidates with
>absolutely identical opinions. Tideman's definition of clones
>is too strong (because he supposes that clones must no be
>ranked identically to non-clones by any voter), so that
>his definition of clones is -to my opinion- not meaningfull
>enough.
>
>Markus Schulze
>
>