[EM] Hello again -- and a new method for you!

[Ernest Prabhakar]

On Apr 12, 2004, at 12:07 AM, Jobst Heitzig wrote:

> The difference to Tideman is that the river method lets a strong 
> defeat,
> say Y>X, contradict a weaker one, say A>B, only if that strong defeat 
> is
> relevant to decide whether X wins or not. When X is already defeated by
> another, even stronger defeat, say Z>X, then Y>X is not used and the
> weaker defeat A>B gets a chance to decide between A and B. On the
> contrary, Tideman would keep both Z>X and Y>X and drop A>B
> unnecessarily. Methods which resolve cycles of weak defeats before
> cycles of strong defeats will drop A>B before even looking at the
> relationship of Y>X and Z>X!

Hmm, very interesting. Thanks, that helps clarify things.

My personal view is that election methods should be considered a form 
of information encoding, and thus the optimal method is one which loses 
the least amount of information.  I'm curious whether there's any way 
to measure whether the River method actually manages to retain more 
relevant information than Tideman.  Steve Eppley, where art thou?

> As a side effect, the resulting diagrams are much more simple and
> intuitive with the river method (they are essentially tree-shaped) than
> with Tideman (where they can be any acyclic graph) or versions of
> sequential dropping (where they can still contain cycles, since they
> stop when the first option becomes undefeated).

Hmm, would you mind clarifying that?   Is your point that the River 
method starts with a single 'root' of the tree, and only builds on 
there, while Tideman allows multiple roots?

If so, that would certainly be interesting, as one of the challenges I 
am wrestling with for MMV is how best to represent these multi-root, 
uncorrelated matchups.   If there was a way to avoid that, while still 
preserving other benefits, that would be good to know.

Has anyone come up with any significant criteria which the River does 
NOT meet, but other Tideman derivatives do?

-- Ernie P.

>
> Jobst
>
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