[EM] Stronger than LIIA

[Matthijs van Duin]

Hi list,

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 ;-)

  - xmath

-- 
Matthijs van Duin  --  May the Forth be with you!