[EM] SciAm article

[Steve Eppley]

Forest Simmons wrote:
> On Wed, 18 Feb 2004, Steve Eppley wrote:
> > Forest Simmons wrote:
> > -snip-
> > > They also express the belief that the completion method
> > > doesn't matter too much because according to a theorem
> > > of Black, Condorcet cycles should be rare in political
> > > elections.
> >
> > If that's Black's "median voter" theorem, it assumes the
> > candidates take positions on a 1-dimensional spectrum.  A
> > rather bold and shaky assumption, in my opinion.
> 
> They do quote this one dimensional spectrum condition, but 
> also allude to another theorem of Black (as well as other
> theorems) that gives other conditions for the existence
> of a CW.  For example, they claim that if the leading
> contenders are controversial enough to be ranked mostly
> at the extremes of the ballots, then there will be a CW,
> no matter the dimension of the issue space. 

If most voters rank the leading contenders at the extremes 
of their sincere orders of preference, it's a sign that the 
voting method is highly prone to spoiling.  

So it doesn't follow from that second theorem that 
Condorcet winners will be common, without adding an 
assumption about the voting method being "bad" enough to 
cause many (moderate) potential contenders to choose not to 
compete (to avoid being spoilers).  That assumption doesn't 
make sense in the authors' context, since they're arguing 
that much better methods exist.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)