Unless I'm mistaken, the method called "Random Favorite" is cloneproof,
for an extended variant of independence from clones that says that the
probability of a clone set member being chosen can not depend on the
size of the clone set.
Say the first ballot is chosen. Then before cloning, the first choice is
obviously picked. If the first choice was part of a clone set and the
clone set is either made larger or smaller, a member of that clone set
is still picked. So Random Favorite appears cloneproof.
The other two random strategy-proof ranked methods we know of - Random
Pair and Random Candidate - are not. Random Candidate is obviously
vulnerable to teaming. So is Random Pair, because adding clones means
there's a greater probability one or both of the pair come from the
clone set.
However, there is a rated method that is also strategy-proof. It is
called Hay voting. Some time ago, I stumbled across
http://www.panix.com/~tehom/essays/hay-extended.html , which seems to be
a proposal to make Hay voting cloneproof. I haven't really understood
the details yet, but I'm wondering if this could be used to also make
the two Random methods cloneproof.
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