[EM] Stronger than LIIA
Matthijs van Duin
eme at nubz.org
Tue Mar 6 10:42:36 PST 2007
I came up with a criterion for ranked voting systems. I think it is
new, though if it isn't I'm sure someone will point that out to me :-)
Criterion: Adding a candidate who is pairwise defeated by the current
winner may not cause a different winner to be chosen.
Equivalently: If removing a candidate causes a different winner to be
chosen, the new winner did not pairwise defeat the removed candidate.
Intuitively the criterion feels right... if a new candidate shows up but
is immediately defeated by the current winner, it's "nice of you to
come, and thank you for playing, but..."
This criterion implies Local Independence of Irrelevant Alternatives,
and hence Smith, Condorcet, Mutual Majority, etc. It appears stronger
than LIIA though: if a new candidate is added who is defeated by the
current winner, but itself defeats a candidate who defeats the current
winner, then the new candidate is part of the smith set, so LIIA allows
for a different outcome, but my criterion demands that the outcome
remains the same.
It's also attainable: Definite Majority Choice complies with this
criterion, as do similar pairwise sorted methods. I haven't checked
other methods yet, it would be interesting to see which ones comply, and
even more interesting to see a concrete case that complies with LIIA but
violates my criterion...
Also, can anyone think of a good name for it? I think "Strong Local
Independence of Irrelevant Alternatives" is getting a bit verbose ;-)
Matthijs van Duin -- May the Forth be with you!
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