# [EM] Possible Multi-Winner Pairwise techniques/algorithms (Part 3)

Gervase Lam gervase.lam at group.force9.co.uk
Sat Jun 4 07:53:55 PDT 2005

In the Parts 1 and 2, the 'seeds' are ballots.  The winners come/develop
from these seeds.

The problem with this is that the methods I discussed do not guarantee n
winners.  So, I decided to take it from another direction.  What if the
"seeds" were the candidates themselves.

If each candidate x were given the ballots that have x ranked first, when
the ballots that candidate x has are tallied up into a pairwise matrix,
candidate x would be the MMPO winner.  (I chose MMPO, because it is a
simple method.  Also note that candidate x is the Condorcet winner in this
circumstance.)

But this is not fair as some candidates have more ballots than other
candidates.  What we need to get to is for n candidates to have N/n
ballots each, where N is the total number of ballots (i.e. voters).
However, those N/n ballots that each candidate x has must have x as the
MMPO winner.

So, what if a candidate x has more than N/n ballots?  It could be deemed
that the candidate has a sufficient number of ballots to be elected.  That
means that the candidate does not need to contest the election any
further.  So, the ballots that were against candidate x are moved to the
the candidates that are ranked next on the ballots.

I then realised that this was basically STV.  If I hadn't have learnt
about the basics of how STV worked so recently, may be I would have
realised more quickly what was going on.

This begs an interesting question.  If there were to be an STV election,
but you were allowed to choose a pairwise method to determine which
candidate should be eliminated at each stage, what pairwise method would
you choose?

Thanks,
Gervase.