[EM] Fw: borda count

[Steve Eppley]

Hi,

Stephane R wrote:
> To the possible exception of how one counts truncated ballots...
> If you assume all ballots are full rankings Steve is right.
> However, some treatments proposed on this list for truncated 
> ballots could produce different winners in case of equal
> ranks or partial rankings...
> I promote treatment of such cases that end up with the
> same total points as a fully ranked ballot. With any ballot
> producing the same number of points, Steve is right.

I assume Stephane is right.  I don't know all the Borda 
variants that've been proposed on this list, but the 
handling of non-strict orderings can make a difference.  

I don't know if the Duc de Borda considered the possibility 
of non-strict orderings.  If my memory is correct, his 
formula was to award to each candidate the number of  
candidates the voter ranked below it. (This is like
3-2-1-0 except for candidates ranked as equals.)  
Given N candidates, a candidate ranked uniquely top 
would receive N-1 points from that ballot.  Taking 
the formula literally, if two candidates are ranked 
equal at the top they would each receive N-2 points.  

John Duggan taught a different definition of the Borda 
count that he prefers:  Each candidate scores the number 
of candidates ranked below it minus the number ranked over 
it.  This variation elects the same as the variation that 
awards to each candidate the number of candidates ranked 
below it plus half the number ranked equal to it.

--Steve