[EM] Democratic symmetry

[Rob Lanphier]

To whom it may concern,

While I'm pleased that The Economist has chosen to tackle the subject of
electoral system fairness in the March 4 edition of The Economist ("The
mathematics of voting: Democratic symmetry", p.83), it saddens me to see
an uncritical look at the work of Dr. Donald Saari.  Dr. Saari's work has
been the subject of many a discussion on the Election Methods mailing list 
[1], and the commentary has rarely been flattering.  

The method that Dr. Saari proports as the fairest method, the Borda count,
presupposes a very narrow definition of fairness.  While focusing on
abstract concepts of symmetry and cancellation, he misses the boat on more
important criteria, such as the "Majority Winner Criterion", which states
that if a strict majority of the voters rank a particular alternative as
their first choice, then the voting method must select that alternative
as the unique winner [2].  Nearly all other methods proposed by electoral
reformers pass this criterion, not to mention first-past-the-post.  The
Borda count is one of the few methods that doesn't.

Dr. Saari deserves a pat on the back for persisting in the face of Kennith
Arrow's famous thereom, which suggests that there is no perfect voting
system.  Many in Dr. Saari's field have used this thereom as an excuse for
not finding better alternatives to first-past-the-post; Dr. Saari has
rightly chosen to question the basis of the theroem by pointing out
problems with it (for instance, the Independence from Irrelevent
Alternatives Criterion has been questioned by Dr. Saari and others who
study these matters).  However, Dr. Saari goes too far by rejecting many
other completely reasonable criteria.

There are many systems which stand up to much more stringent criteria than
Borda does, such as those methods proposed by Copeland, Fishburn, Kemeny,
Schwartz, Smith, Hare, Coombs, Condorcet, and others.  These methods were
constructed with an eye toward many other more important criteria than
"symmetry", and deserve a fairer treatment by your publication than the
glib writeoff of not being the "only system that fits the bill".

I'm also disappointed that this article was not selected for posting
online.  I've posted a relevant snippet to the mailing list, and a lively
discussion is already ensuing.[3]  I encourage you, Dr. Saari, and your
readers to participate in the debate about this subject.

Thank you,
Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla

[1]  Election Methods Mailing list: http://www.eskimo.com/~robla/em
     Past discussions of Dr. Saari's work:
     
[2]  Anderson, L.B., "A Partial Ranking of Selected Voting Methods Based
on Majority, Condorcet, and Monotonicity Criteria"  Position Paper, March
17, 1996. Author Affiliation:  Institute for Defense Analyses, Alexandria,
VA.

[3]  There's already been many discussions about Dr. Saari's work on the
Election Methods List.  Here's links to the latest:

    Discussion about the Economist article, March 5, 2000:
    http://www.eGroups.com/group/election-methods-list/showthread.html?start=5117

    "Re: IIA Theory" - October 5, 1999
    http://www.eGroups.com/group/election-methods-list/4336.html?

    Quote from this thread:
    "By going through Sen's, Gibbard's and Satterthwaite's work first you
    can see how Saari's criticism of IIA as being 'absurd' (because, and
    this should already obvious, it fails to be satisfied in all cases) is
    itself problematic, especially in its "implications" towards Borda
    score systems, and at the same time how right Saari is in seeing that
    Arrow's theorem has at its heart the simple problem of IIA
    occasionally failing to be satisfied where more than two voters have
    an impact on the outcome."
    -- David Catchpole

    Re: Approval Voting fish (2) - March 3, 2000
    http://www.eGroups.com/group/election-methods-list/5093.html
    Quote from this thread:
    "Borda, in all the proposals that I've heard of, requires you to give
    points to all but one of the candidates, no matter how much you
    despise your 2nd to last choice, and your other lower choices.  That 
    doesn't happen with any other proposed method, and doesn't even happen 
    with [first-past-the-post]"
    --- Mike Ossipoff