[EM] SciAm article

[Steve Eppley]

Forest Simmons wrote:

-snip-

> The authors eloquently promote the CW as the true majority 
> winner, and explain their theorem that methods that do
> not choose the CW are further from satisfying the IIAC
> than methods that do. 
> 
> They also express the believe 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.  I think 
the widespread view that candidates are arrayed along a 1-
dimensional "liberal-conservative" spectrum has been 
induced by the long term use of primitive voting methods, 
which force candidates trying to win to belong to one of 
two (or a few) big parties, and more or less toe the party 
line.

Charlie Plott's theorem shows that when the issue topology 
is at least 2 dimensions, then it's almost always the case 
that for every point in the issue space, there exist an 
infinity of other points that are preferred by a majority. 
(In other words, no point is a Condorcet winner.)  Of 
course, there aren't an infinity of candidates in public 
elections, but candidates can choose their platform point 
and are motivated to find a platform that will be preferred 
by a majority over their leading rival's platform.

> Also the authors express the opinion that strategic 
> considerations are more of a concern in small group
> voting and not so much in large scale elections. 

If they are referring to voting strategies, that may be 
true, since many people aren't strategically-minded.  But 
we must also consider nomination strategies, which is why 
"independence" criteria are important.  In large public 
elections, the stakes are high enough that nomination 
strategies will be employed if they are expected to be 
effective.

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