[EM] Easy River definition (also my site is back up)

[Kevin Venzke]

Hi Mike and everyone,

First off, if anyone was missing my site, it is back up. I had to find different
hosting (a bit abruptly).

Where I was trying to link right before the site went down:
votingmethods.net/cond
works out a given (or random) scenario for Schulze, RP, or River. You just have to
expand sections at the bottom of the result. So it could be worth a look.

Mike wrote:
> Is River as easy to define &. explain as RP?.

I see I should try to write out clearly how I suggest to understand River.

There is no "final ranking" in River. Instead every candidate begins "below no one"
or "subordinated to no one." This is sort of a ranking but the "trees" we make go
only one level down: you will never be able to ascend two positions from a given
candidate.

1. Initially each candidate is subordinated to no one.
2. Consider each pairwise defeat from strongest to weakest.
3. When you consider a defeat, ask whether the loser is subordinated to anyone?
If so: Ignore the defeat and proceed to the next.
If not, then ask:
4. Is the defeat winner subordinated to the defeat loser? If so, ignore the defeat
and go to the next.
5. Is the defeat winner subordinated to someone else? If so, the defeat loser, along
with everyone subordinated to them, becomes subordinated to the candidate that the
defeat winner is subordinated to.
6. Otherwise it must be that the defeat winner is subordinated to no one. So here
the defeat loser, along with everyone subordinated to them, becomes subordinated to
the defeat winner.
7. End loop. Go to the next defeat.
8. In the end, the candidates subordinated to no one are the winners.

Alternatively instead of talking about subordination, you can say that each
candidate has their own "bin" and starts in their own and may move to another.
This would allow you to merge steps 4 and 5:
"4. The defeat loser, along with everyone *in the loser's bin*, moves to whichever
bin the defeat winner is currently located in."
And if the latter bin happens to be the loser's bin, in effect nothing happens. We
don't need a rule saying to ignore the defeat, because the bin movement doesn't
change anything either.

I can understand if a reader eyeballs all that and says this looks like a mess and
it's not clearer than RP.

But hear me out on the *ease* of it:

1. If you are programming River, you never actually check for a cycle, whether a
proposed defeat would create one. And comparing to Schulze, you never trace a
beatpath or find its strength, or (by its other algorithm) have to find the Schwartz
set repeatedly.
2. If you are solving it by hand, it would be enough to have a fridge magnet for
each candidate, start them out in imaginary bins, and push the magnets around in a
straightforward way to track who is subordinated to whom.

It may be possible to define RP more concisely, but it takes some work to figure out
what it is actually saying to do to solve it.

Hopefully the above explains it better than I have before.

Kevin
votingmethods.net