[EM] Matthijs van Duin criterion

[Matthijs van Duin]

On Wed, Mar 07, 2007 at 09:48:55AM +0100, Jobst Heitzig wrote:
>E.g., every method which picks from the Copeland set will do

Could you sketch an outline for that?  I don't immediately see it from 
the definition of Copeland set I looked up...


>so far I'm happy that DMC is again fulfilling naturally a new criterion

Indeed.

BTW, here's an outline of why DMC does comply, which I hadn't given yet:

Say we add a candidate who is defeated by the current winner...

If the new candidate has lower approval than the current winner, he's 
strongly defeated and immediately disqualified.

If the new candidate has higher approval than the current winner, then 
the current winner is still the least approved candidate who defeats all 
higher approved candidates, so still wins.


>while other methods seem to have problems with it.

And another bites the dust... M arginal Ranked Approval Voting, though 
only a slight variation of DMC, fails my criterion:

11      X > W > Z >> Y
8       W > Z > Y >> X
7       Y > X > W >> Z
6       Z > Y > X >> W

approvals:  26 W,  25 Z,  24 X,  21 Y
defeats:  26 W>Z,  25 Z>Y,  24 X>W,  21 Y>X,  19 W>Y,  18 X>Z

MRAV elects W, but removing Z causes the winner to change to X, who 
defeated Z in violation of my criterion.

DMC would have elected X in the first place.


How about naming it the "Entry Bar Criterion", given that it seems to 
impose a fairly steep one on new candidates, as well as on voting system 
themselves it seems ;-)


  - xmath

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