Lorrie Cranor's paper (Re: Coombs' Method)

[Steve Eppley]

Rob L wrote:
-snip-
>    voter 1: a b c d e  
>    voter 2: b c e d a
>    voter 3: e a b c d
>    voter 4: a b d e c
>    voter 5: b d c a e
>
>Given this preference profile, a is the Condorcet winner. However,
>an examination of the number of times each alternative is ranked
>first, second, etc., bears the following results: 
>                                       a  b  c  d  e
>    Voters ranking alternative first:  2  2  0  0  1
>    Voters ranking alternative second: 1  2  1  1  0
>    Voters ranking alternative third:  0  1  2  1  1
>    Voters ranking alternative fourth: 1  0  1  2  1
>    Voters ranking alternative fifth:  1  0  1  1  2
>
>In an examination of rankings, b appears to be the best choice --
>with equal first ranks to a and more second and third ranks than a
>-- yet the Condorcet winner is a. 

The unstated assumption about the "appearance" that b is best is
that the *gaps* between successively ranked candidates on each ballot
are about equal.  In other words, the assumption is that the
preference orders imply ratings something like:
  1st choice:  100
  2nd choice:   75
  3rd choice:   50
  4th choice:   25
  5th choice:    0
If you then sum the ratings, choice b has the highest total (400).

But there's no basis for assuming any particular ratings given only 
preference orders.  The info is missing from the ballots.

Mike has pointed out that Borda's method can violate majority rule in
that it can defeat a candidate which is first choice of a majority.
I'm not sure if that's intended to be a negative criticism of Borda
and other point systems.  I reject Borda because it assumes ratings
which aren't really contained in the ballots, and I reject rating
systems because they invariably create strong incentives for voters
to misrepresent their true ratings and because there's no way to
compare voters' rating scales to know the scales have the same
meaning to each voter.  But in a scenario where it is somehow known,
maybe through divine intervention, that the voters sincerely rated
the choices on the same scale with the above "0 to 100" ratings, 
I wouldn't argue that choice b is a bad choice. 

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