[EM] Re: Chain Climbing --> Chain Filling

[Russ Paielli]

Jobst Heitzig heitzig-j-at-web.de |EMlist| wrote:
> Dear Ted!
> 
> You wrote:
> 
>>Thanks to both of your responses, I have an idea now that I think will work,
>>and it should have (my) desired quality of encouraging generous approval
>>cutoff and ranking of candidates below the cutoff.
>>
>>Basically, the idea is simply Beatpath:  Break each cycle at the weakest link.
>>But what should be the weakest link?  Why not call it the defeat made by the
>>candidate with lowest approval?  We could call this Total Approval 
>>Beatpath (TAB), but suggest a better name if you want.
> 
> 
> I now remember what conclusion I came to about this idea when I first
> thought about it some months ago: It will always elect the least
> approved candidate which beats all more approved ones. Proof: (i) The
> winner, say X, beats all more approved ones; assume otherwise that Y
> beats X and has more approval; then the beatpath Y>X is stronger than
> all beatpaths X>... . (ii) No candidate with lower approval than X can
> beat all more approved candidates; assume otherwise that Y beats all
> more approved candidates and has less approval; then the beatpath Y>X is
> stronger than all beatpaths ...>Y. This proof applies not only to
> Beatpath with your definition of defeat strength but to all immune cycle
> breaking methods (Beatpath, River, Ranked Pairs, ...) with your
> definition of defeat strength.
> 
> In other words, this is the same method as Kevin's!

Which method of Kevin's are you referring to?

--Russ