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

[Ted Stern]

On 14 Mar 2005 at 07:10 PST, Kevin Venzke wrote:
> Dear Jobst,
>
> --- Jobst Heitzig <heitzig-j at web.de> wrote:
>> Dear Ted!
>> > 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 was thinking about this when writing the grand compromise proposal but
>> didn't propose it for some reason I don't remember, so I should give it
>> another thought. Did you prove any nice properties yet?
>
> I suggested this measure of defeat strength when I proposed an easy way
> to hand-count three-slot Condorcet, since by that method the WV information
> isn't preserved. I believe you didn't like this measure because it seemed
> unintuitive to elect anyone other than the approval winner when there is
> a three-candidate cycle.
>
> Kevin Venzke

Hi Kevin,

I'm not sure Jobst has analyzed my method correctly.  Is this equivalent to
what you proposed?

   "Rank candidate 'seeds' in descending order of approval.  For a
    candidate to move up in rank, it has to defeat all higher seeded
    teams in succession, and only after each of those has itself moved
    up in rank as much as possible."

See also my Total Approval Ranked Pairs message posted earlier.

Ted
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