[EM] cloning - how Woodall dealt with the issue

Warren Smith wds at math.temple.edu
Sat Jan 27 14:51:03 PST 2007

Clone-Winner: Cloning a candidate who has a positive probability of 
election should not help any other candidate.

Clone-Loser: Cloning a candidate who has a zero probability of election 
should not change the result of the election.
More precisely, I think this means all victory-probabilities are unaltered.

Clone-immune: satisfy both of the above.

Douglas R. Woodall:
Monotonicity of Single-seat Preferential Election Rules,
Discrete Applied Mathematics 77,1 (1997) 81-98.

I think these are good.  However, I feel that Woodall's criteria were too weak.
It seems to me you could strengthen them by adding, e.g.

Clone-unequal:  cloning a candidate B who is never ranked equal to any other
in any ballot, leaves all election-probabilities unaltered (eexcept for splitup among
the clones).

to the defintn of "clone-immune."

Also, I think when dealing with range-type ballots we should pre-assume an infinitesimally small
random pre-perturbatio of all votes, so we don't have to concern ourselvs with exact ties,
etc (reduces to zero probability) - I here as usual speak of continuum range voting.

Warren D Smith

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