[EM] Stronger than LIIA

[Matthijs van Duin]

On Tue, Mar 06, 2007 at 07:57:51PM +0100, Markus Schulze wrote:
>Dear Matthijs van Duin,
>you wrote (6 Mar 2007):
>> Criterion: Adding a candidate who is pairwise defeated by the 
>> current winner may not cause a different winner to be chosen.
>>
>> (...)
>>
>> This criterion implies Local Independence of Irrelevant 
>> Alternatives, and hence Smith, Condorcet, Mutual Majority, etc.
>
>The MinMax method satisfies this criterion.
>However, the MinMax method violates Mutual Majority.

Not possible... my criterion implies Smith (implies Mutual Majority):

Start with the smith set, from which a winner is picked.  Every 
candidate you now add will be defeated by the winner (by definition of 
the smith set), hence will not change the winner.  Conclusion: for every 
election, the winner is picked from the smith set.

Alternatively, assume the winner is picked from outside the smith set.  
Now remove the winner.  By my criterion, the new winner may not defeat 
the old one, which means it can't be in the smith set either.  However, 
repeating this process, eventually you'll run out of candidates outside 
the smith set and you'll have a contradiction.

  - xmath

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