[EM] which voting methods fail WMW?

[Chris Benham]

Warren Smith (Wed.Oct.5):

>wds:
>>> Robla failed to mention that range voting *does* obey a weakened form of
>>>the majority-winner criterion (call it "WMW").  Specifically:
>>>    "If a strict majority of the voters regard X as their unique favorite, then
>>>   they, acting alone without regard to what the other voters do, can force his election."
>>>I don't know about you, but I personally regard WMW as a more-desirable critrion for
>>>a voting system to obey, than Anderson 1994's MW criterion.
>  
>
>
>  
>
>>>Chris  Benham:
>>>Are there any  methods actually  *fail*  this criterion?   Borda perhaps?
>>    
>>
>
>--response by wds:
>yes, Borda fails it.  So does the somewhat Borda-like method used
>on the Island of Nauru.  So does Coombs' IRV-like voting method.
>Also Ken Arrow's favorite voting method (or so I heard) the Arrow-Raynaud method,
>fails this test.
>
>Range voting, however, passes this test.
>wds
>

Warren,
I've seen  Coombs defined with and without a majority-stopping rule. (To 
me not having it seems worse and odd). I assume you are referring to the 
version without:
http://cec.wustl.edu/~rhl1/rbvote/desc.html

> The candidate with the largest last-rank total is eliminated.  The 
> last-rank totals are recalculated and the step repeated until only one 
> remains. 

The other version seems more common:
http://wiki.electorama.com/wiki/Coombs%27_method

> Each voter rank-orders all of the candidates on their ballot. If at 
> any time one candidate is ranked first (among non-eliminated 
> candidates) by an absolute majority of the voters, then this is the 
> winner. As long as this is not the case, the candidate which is ranked 
> last (again among non-eliminated candidates) by the most (or a 
> plurality </wiki/Plurality> of) voters is eliminated.
>
BTW, do you know for sure that one of these definitions is incorrect?  
Obviously  the version with the stopping-rule meets your WMW criterion.

I am sure that  "Arrow-Raynaud"  is the same as plain "Raynaud" 
(sometimes spelt "Reynaud") which is a method that meets the Condorcet 
criterion.
What according to you is its definition, and can you give an example of 
it failing your WMW criterion?


Chris  Benham






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