Condorcet(x( ))

[Steve Eppley]

Lucien Saumur wrote:
>          I do not understand what you mean by vote-against.
>
>          I understand Condorcet to compare each candidate
>to every other candidate. Whether you count the unranked
>candidates as having obtained .0 or .5 vote against each
>other does not change the result of the comparison.

Yes it does.  It won't change which candidate wins the pairing, since 
both are hurt equally by the equal votes against.  But when Condorcet 
measures the size of a pairwise defeat it doesn't use the margin of 
difference.  It simply uses the votes for the pairwinner as the size 
of the pairloser's defeat.

>          Example: if 85 of 100 voters do not rank A and B
>while 10 voters prefer A to B and 5 voters prefer B to A,
>the result will be the same (i.e. A beats B) whether we
>consider that A beats B 10 to 5 or (10 + 42.5) to (5 + 42.5).

With x=0:  The size of B's defeat = the votes for A = 10
With x=.5: The size of B's defeat = the votes for A = 52.5

If B's worst defeat is A vs B, then A's worst defeat cannot be A vs B.  
So the 85 equal votes hurt B more than A.

--Steve