[EM] FWD: Borda Count by Paul Dumais

[Donald E Davison]

  -----------Forwarded letter -------------
Date:   Fri, 16 Apr 1999 10:22:44 -0600
From: Paul Dumais <paul at amc.ab.ca>
Reply-To: paul at amc.ab.ca
Organization: AMC
MIME-Version: 1.0
To: Donald E Davison <donald at mich.com>
Subject: Re: Salva Voting - multi-seat example

Hi,

        In response to this, I'd like to discuss Borda Count. Sorry if this is
somewhat off topic. I think Borda count is clearly the best choice
(clear to me at least ;-)). The best way I to convince others of this is
by many examples and comparissons with other voting methods. Looking at
Borda count, I have never found an example of an "innapropriate" result
or a result which was more "appropriate" via another method. There has
been several mentions of borda count having it's second and subsequent
choices working against your first. I feel this is appropriate. Your
second choice is an inication of compromise. Where a race is close
between several candidates, often the first choice count gives close to
a tie (two or three way). Second and subsequent choices here are all
important. Borda count is similar to STV and condorcet, but more fare.
Condorcet is like stv except the "lowest" candidate does not have his
votes transferred. All votes are transferred to all combinations of
pairs. The choice of the "lowest" candidate using the first choices is
unfare and not necessary. Borda count is similar to condorcet in that
one vote is given to a candidate for each paring it wins. Condorcet
breaks up the votes ito pairing though, which wastes votes. I will
provide in-detail examples in later posts to clarify this.
        A description of how Borda count should work: Each voter ranks his
candidates ie ABC. He need not rank them all. He could only give one
choice if he wanted. Suppose there are 5 candidates, a vote of ABC would
give A - 4
B - 3
C - 2
D - 0.5
E - 0.5

Notice that D and E split the remaining points since they were not
ranked. This point system is equivalent to a round robin tourney where a
point is given for every match one. Since ech candidate has 4 matches,
ech candidate gets 0-4 points. D and E tie, so 0.5. All ties get 0.5. So
if someone votes AD, the points would be:
A-4
D-3
C-1
D-1
E-1

Each candidate is given an appropriate number of points for each vote.
After the points are added for each voter, the ranking of candidates is
easily made. The top vote-getters get the available seats - simply and
fairly. Borda count is better than Salva voting, not all the votes are
used equally in any method which transfers votes. The "lower candidates"
get there votes transferred. The choice of "lower candidates" is unfair.
The first choice of the voters might reveal a very close race, but there
may be overwhelming support for a candidate when looking at second
choices. Yet, for single seat elections, the Salva method might transfer
the votes of those who chose this popular candidate as their first
choice. Transferring votes will always be unfair, because any fair
measure of the "lowest candidate(s)" will also be a fair method of
choosing the "highest" candidates, which eliminates the need to transfer
votes in the first place. Borda count is such a method.
        I can construct examples where borda count is superior to other
methods. I have not found any examples where other methods are superior
to borda count. Perhaps someone can help.