[EM] Round Robins

[Dave Ketchum]

On Tue, 15 Mar 2005 06:53:52 +0100 Jobst Heitzig wrote:

> Dear Dave!
> 
> You wrote:
> 
>>Agreed you do not need (n-1)*n/2 pairwise comparisons BUT, seems to me
>>ROWS went too far:
>>     It will happily and efficiently return the CW if there is one.
>>     It does not know if there is a cycle, though the winner of the n-1
>>comparisons will, at least, be a cycle member.
>>
>>Easiest I can think of is another n-1 comparisons to see if the apparent
>>winner is CW or only a cycle member and, if a member, keep going til you
>>have the complete cycle.
>>
> 
> That's a nice suggestion for the "justification" step of the method but
> it doesn't change the winner. Or did you mean to say that a method
> should not elect a candidate unless it "knows" in which defeat cycles
> s/he is?
> 
> Yours, Jobst
> 
I suspect I did not emphasize enough so, assume we are doing only n-1, 
A should win, the cycle is A>B>C>A, and C is the first member found (does 
not matter if there is a D, for such will be discarded as soon as we have 
a cycle member).
     PROVIDED B is the next cycle member, it will take over and 
recognize A as final winner when found.
     BUT IF A is the next cycle member, C will reject it and accept B as 
final winner when that is found.

-- 
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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