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

[Jobst Heitzig]

Hi Ernest!

you wrote:
> On Apr 11, 2004, at 2:52 PM, Jobst Heitzig wrote:
> 
>> Hi again!
>>
>>> http://radicalcentrism.org/majority_voting.html
>>
>>
>> So this is essentially Tideman - right?
> 
> 
> Yes, Tideman, like MAM-d and Eppley's.   Just some minor variation in
> how it handles same-sized majorities.
> 
> I think your River method is most like Tideman, is it not?
> 

It has the same spirit of resolving cycles of strong defeats before
cycles of weak defeats while all versions of sequential dropping do the
opposite.

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!

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).

Jobst