[EM] RP vs River

[Michael Ossipoff]

 Oops! I forgot to include this topic in my previous post:

RP vs River:
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It seems to me that River clearly does better than RP toward the goal
of not avoidably meaningfully disregarding a public pairwise decision
(a pairwise defeat).

If X>Y, and Z>Y, and the Z>Y defeat is stronger than the X>Y defeat,
and is therefore considered sooner, and kept, in River,

...and therefore the X>Y defeat isn't kept, in River, because it
duplicates an already-kept defeat, the Z>Y defeat,

...then the stronger, already-kept, Z>Y defeat does fully as much
(more, actually) toward keeping Y from winning as would the weaker,
unkept, X>Y defeat.

Therefore, the X>Y voters aren't losing anything when X>Y isn't kept.

...But, if A>B cycles with X>Y, then the A>B defeat would be skipped
in RP. But not in River, because X>Y isn't kept.

Therefore, RP unnecessarily disregards a public pairwise decision
(A>B) that River doesn' disregard.

That suggests that River is better than RP

I don't know what those 2 methods' various criteion-compliance
differences are. On what important strategy criteria do they differ?

What are the best arguments for RP over River.

I've heard that RP can choose outside the Schwartz set. Aesthetically
it's desirable to choose from the Schwartz set, but it's hardly
necessary. If X is in the Smith set, but not the Schwartz set, then
the voters have said that X is just as good as one of the Schwartz set
members.

It would be nice to choose from the Schwartz set, but the price is
Beatpath's poorer consistency, and its premature, incompletely tested
choice. RP and River build a consistent structure, of the strongest
mutually consistent public pairwise decisions.

What are the strongest argumnts for RP over River.

The best one that I know is brevity and simpliity of definition.

If i were proposing RF or River (for ideal majoritaian conditions),I
might very well propose RP, due to its somewhat greater
simplicity,even though River seems better.

Michael Ossipoff