[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.
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