[EM] Re: proper Borda implementation

[James Gilmour]

Jeffrey O'Neill > Sent: Sunday, September 26, 2004 3:25 AM
> 
> >> (1) C and D each get nothing.
> >> (2) C and D each get 1.5 points (average of leftover points).
> >
> > I believe that's why he was asking here.  That said, I don't think 
> > there's a right answer.  I've looked into this before and Borda 
> > advocates usually say that Borda requires full ballots, end 
> of story.
> 
> 
> If Borda advocates insist on full ballots (presumably to 
> lessen the effects of strategic voting), then (2) seems like 
> the best choice for dealing with incomplete ballots.

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.

James