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

[Jobst Heitzig]

Hi again, Markus!

you wrote:
> could you please post an example where your river method
> differs from my beatpath method (aka Schwartz Sequential
> Dropping, aka Cloneproof Schwartz Sequential Dropping)?

Here's the example where our old common favourite (I don't mean to enter
a "copyright discussion" here...) differs from the new method (if it is
new which I'm not sure since it might turn out equal to some well-known
other method...):


Number of deciders	...over...				
preferring...		A	B	C	D		
		A	-	e	small	a
		B	small	-	c	f
		C	d	small	-	small
		D	small	small	b	-

		with a > b > c > d > e > f (> all small values)

PC, SC, SD, SSD drop f and e so that B wins.
Tideman adds all but d so that A wins.
River method adds a and b, skips c since C is already defeated, skips d
since that would give a cycle, adds e and finally skips f since D is
already defeated. Here also A wins: C --b--> D --a--> A! <--e-- B


Together with the previous example, this shows that the river method is
different from PC, SC, SD, SSD, and Tideman.

PS: Did anyone ever list all 720 (up to relabeling of A,B,C,D)
possibilities of defeat order for four options A,B,C,D in which the
Smith set is A,B,C,D? That would make a nice test suite...

Frohe Ostern!
Jobst