[EM] SciAm article

[Forest Simmons]

On Wed, 18 Feb 2004, Joseph Malkevitch wrote:

> Dear Steve,
>
> I do not want to speak for what Forest may or may not have meant but in his
> work on elections Duncan Black endorsed a method, sometimes called Black's
> method, which operates in the environment where voters produce ballots where
> all condidates must be ranked on an ordinal ballot and one is allowed to have
> ties between candidates, the goal being to elect a single winner. Black
> suggests that the winner should be the condorcent winner if there is one, and
> if there none that one use the Borda count to get a winner.
>
> Best wishes,
>
> Joe Malkevitch


I'm sure that the authors were influenced by Black in this regard, too,
but Steve was right about (one of) the theorems of Black that they were
referring to.

Forest


>
>
> Steve Eppley wrote:
>
> > 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)
> >
> > ----
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>
> --
> Joseph Malkevitch    |
> Mathematics Dept.    |
> York College(CUNY)   |
> Jamaica, NY 11451
>
> Phone: 718-262-2551
> Web page:
> http://www.york.cuny.edu/~malk
>
>
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