[EM] Simmons cloneproof method is not cloneproof

Chris Benham chrisjbenham at optusnet.com.au
Tue Jan 2 07:26:22 PST 2007

One serious disadvantage that the new Simmons method (in pure form) has 
is that it has a nasty Local IIA
problem, and fails what I might call  "Independence of/from Irrelevant 
Candidates" which says that if there is
some losing candidate X with fewer top preference votes than any other 
candidate and which is pairwise beaten
by every other candidate, then dropping X from the ballots can't change 
the winner. This is a weak criterion that
is easily met by IRV and arguably by all good methods.

02: X>A>B
24: A>B
25: C>A
49: B>C (maybe sincere is B>A or B)

A>B>C>A.  "Simmons" scores: A25,  B24, C49

B has the lowest score and so wins, but if  X is dropped from the 
ballots then B's score rises to 26 and  A wins.
Those two X supporters have a "semi-clone"  split-vote problem.

This problem can be easily patched up by first dropping from the ballots 
all non-members of the Schwartz set before
applying this simple Simmons method  (to give "Schwartz//Simmons").

Warren Smith wrote:

> actually, Simmons is NOT a Condorcet method at all,
> in the sense that it is entirely possible for a unique
> Condorcet winner W to exist, but Simmons does not select W as the unique
> winner, instead claiming that several candidates are tied for winner.
> This usually happens when W has zero top-rank votes.
> I'd pointed that out before but this makes it clearer.
> Similarly, Simmons does not really obey the Smith set property.
My suggested patch would also of course fix this problem.

Chris Benham

More information about the Election-Methods mailing list