[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 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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