[EM] Fw: borda count

James Gilmour jgilmour at globalnet.co.uk
Sat Nov 6 14:22:10 PST 2004

```Mike >Sent: Saturday, November 06, 2004 6:56 PM
>
> Here's a similar question: Does it matter if we use a Borda count of
> 3-2-1-0 (Highest score wins) or 0-1-2-3 (lowest score wins)?
> I thought I read somewhere they weren't necessarily symmetric, but I
> can't think of
> any counterexamples so I might be mistaken. I *do* think the lowest
> score wins version makes it easier to compare elections with varying
> numbers of candidates if you are going to use the Borda count anyway.
>

Here's a comment I posted to this list on 26/09/2004 in response to an earlier query.

I don't have access to a copy of Borda's paper (delivered on 16 June 1770, published in 1781), but I
suspect these problems arise from more recent re-workings of Borda's method.  Is there a copy of the
original paper somewhere on the web?  I searched but found nothing.

He appears to have suggested the method described by Paul in his post on 25/9/04, eg if 4
candidates, on each ballot paper award 3 points to first preference with a diminishing number of
points for each successive preference marked.  So unmarked candidates automatically receive "null
points" (comme on dit en francais).  The winner is the candidate with the MOST points.  Truncated
ballots do not cause any problem.

But Borda's system has also been presented with preferences scored in the reverse order, ie 1 for a
first preference, 2 for a second preference, 3 for a third preference, etc.  When scored this way,
the winner is the candidate with FEWEST points.  But for this system to work at all, every voter
must mark a preference for every candidate.  Perhaps someone has a reference to when this "reversed
presentation" was first proposed.

++++++++++++++++++++++

But I agree with Steve's comment in his second message of today.  Why on earth would anyone want to
discuss Borda?.  It is fundamentally flawed and should be consigned to the museum of electoral
science, no matter what Don Saari may say.

James

```