[EM] C/D resistant Condorcet methods.

[Kristofer Munsterhjelm]

Here's a Condorcet method that I think retains CT's defection resistance 
while being closer to cloneproof. It is Smith,DSC (but I think DAC would 
also work).

Consider Mike's usual C/D example:

Sincere rankings are

33: A>B
32: B>A
34: C

In DSC, {AB} is affirmed with a strength of 65. Then A wins because it's 
supported by one more voter than B. If the A-voters try to defect by 
voting only for A, that reduces the strength of {AB} to 32 so that C 
wins. Similarly, if the B-voters try to defect by voting only for B, 
that reduces the strength of {AB} to 33 so that C still wins.

If all the clones are in the Smith set, this Smith,D*C resists clones. 
However, it might be possible to set up an example where only some of 
the clones are in the Smith set. I'm not sure.

One could also make an ICT analog. Call the ICT version of the Smith 
set, ISmith. Then ISmith,DSC and ISmith,DAC could be constructed.

Also note that one pays a bit for the resistance in that the method no 
longer picks the optimal candidate when faced with sincere votes that 
happen to look like a partial defection. That is, if voters sincerely 
mean that:

33: A>B (33 prefer A to B and both to C)
32: B   (32 like B alone)
34: C   (34 like B alone)

then it won't elect B. That's unavoidable: the method can't read the 
voters' minds, so it can either elect B in the case above (which would 
mean it isn't resistant to C/D), or it can elect someone else (in which 
case, it is, but fails to pick the optimal "sincere" winner).

In picking A instead of C, it might even support the "count all 
candidates ranked above the winner as Approved" modification.

I suspect that Smith,IRV (and also Alternative Smith) resists C/D (but 
it's not monotone and has all the problems IRV has within the Smith set. 
I also have a vague suspicion that you can't have ISmith (ICT, ICA, etc) 
and clone independence, but I don't know that for sure.