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

[Rob Lanphier]

On Sat, 28 Dec 1996, New Democracy wrote:
> Thank you Mike for telling me about this Coombs' Method.
> 
> If anyone knows where I would be able to get the details of the Coombs'
> Method I would thank them. I am most interested in knowing more about it. I
> tried the internet - but Yahoo came up with zero reference out of their
> Political Section.

Well, right now, this probably will require a trip to the library.
However, there is one resource online that I was going to bring up anyway:

Lorrie Cranor's "Vote Aggregation Methods" paper:
http://dworkin.wustl.edu/~lorracks/dsv/diss/node4.html

This contains the following citations which will have more info:

77 Hannu Nurmi. Voting procedures: A summary analysis. British Journal of
   Political Science, 13(2):181-208, 1983. 

78 Hannu Nurmi. Comparing Voting Systems. D. Reidel Publishing Company,
   Dordrecht, 1987. 

Bruce Anderson has a lot of writing which has a wealth of references to
other material, as well.

Back to Lorrie Cranor's page.  I would encourage everyone to read this. 
It contains some arguments that will be controversial among this group
(though they are mostly citations to other work). In particular, this
criticism of the Condorcet Winner criterion:

    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. 

Before you shoot the messenger here, I'm posting this only as an
enticement to read the material.  This in no means suggests that I don't
have opinions about what is wrong with this example.  Right now, I'm not
interested in participating in a debate about this, but wouldn't mind
being a spectator.

Rob
---
Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla