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

[DEMOREP1 at aol.com]

Rob Lanphier wrote--
Although the Condorcet criterion is a popular means for evaluating voting
systems, there are some situations in which it is not clear that the
Condorcet winner represents the collective choice.

For example, Fishburn [46] presents a scenario in which five voters must
choose between five alternatives (a, b, c, d, e). The voters hold the
following preference orderings (listed from most preferred to least
preferred): 

    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. 
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D-- The 2 times that b is second, he/she is beat by a (voters 1 and 4) . The
time that b is third, he/she is beat by a who was second (voter 3).
Fishburn's example does not mean anything.  The head to head concept is
fundamental whether there are 2 choices or 200 choices.  Nothing magical
happens when there are 3 or more choices.