[EM] Re: Nanson and Borda

[Rob LeGrand]

Rob Speer wrote:
> How do you know that Baldwin and Nanson always choose from the Smith
> set? I can't find a proof of that in the paper, and I can't see an
> inherent reason why they would.

Baldwin eliminates only one at a time, the current Borda loser, which is
never a current Condorcet winner.  So even if all but one are eliminated
from the Smith set, that one that's left will be a current Condorcet winner
and so will win.  A candidate that doesn't start out in the Smith set won't
have a chance.

The same reasoning works for Nanson, except that we must consider the
possibility of having the entire Smith set eliminated in one step.  That
can't happen, though, because the average Borda score for Smith set members
is necessarily higher than the average score for the others (and is
necessarily positive, the way I calculate Borda score), and so at least one
member of the current Smith set is certain to survive to the next round.

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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