# [EM] Interesting use of Borda count

Steve Barney barnes992001 at yahoo.com
Wed Jan 2 18:29:01 PST 2002

```Bart:

Where are these Borda rules? I know they are not in the article by Jean Charles
de Borda, which I referred to in my previous message. I also know that Donald
Saari, probably the worlds leading exponent of the BC, says otherwise.
According to Saari it is essential to treat a bullet vote as an indication of a
weak preference for one candidate and indifference between all of the unmarked
candidates. He recommends giving 1 point to the preferred candidate, and 0
points to all the rest, in such a case. The essential thing is to always give
the same difference to each successive ranking. In _Chaotic Elections_, Saari
suggests that if voters are permitted to give (2,0,0) points to the 3
candidates by bullet voting, they will have:

"an incentive to vote for only one candidate to give the candidate a boost. A
simple way to minimize this strategic action is to interpret the BC as giving a
point differential to each candidate. Thus a truncated ballot assigns only one
point to the candidate."
--Donald Saari, _Chaotic Elections_, pg 151.

This interpretation preserves the nature of the BC as a method based on
pairwise compairisons. Here is excerpt (from an online article) about the way
in which the BC can be interpreted as based on pairwise comparisons:

An important relationship (probably due to Borda and known by Nanson [17])
between the pairwise and the BC tallies can be described by computing how a
voter with preferences A > B > C votes in pairwise elections.
Thus the sum of points this voter provides a candidate over all pairwise
elections equals what he assigns her in a BC election. This means (along with
neutrality 2 and the fact that each pair is tallied with the same voting
vector) that a candidate's BC election tally is the sum of her pairwise
tallies. (See Saari, _Basic Geometry of Voting, Springer-Verlag, 1995
"EXPLAINING ALL THREE-ALTERNATIVE VOTING OUTCOMES," DONALD G. SAARI
http://www.math.nwu.edu/~d_saari/vote/triple.pdf

> Date: Tue, 01 Jan 2002 15:17:21 -0800
> From: Bart Ingles <bartman at netgate.net>
> To: election-methods-list at eskimo.com
> Subject: Re: [EM] Interesting use of Borda count
>
> I wonder if Bennett's ballot was counted per Borda rules -- i.e.
> Bennetts's first choice receiving 10 points, the remaining nine
> receiving 5 points each.
>
> If this were a public election held in Florida, Bennett's candidate
> would have contested the election, claiming that either the election
> method or the voter instructions were at fault, causing Bennett to cast
> non-optimal ballot.  The result being, of course, that Bennett was
> robbed of her voting rights by being allowed to vote incorrectly.
>
>
> Anthony Simmons wrote:
> >
> > Interesting use of Borda count.  Note that one voter insisted
. . .

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"Democracy"?: