[EM] versions of weighted pairwise

[James Green-Armytage]

	I guess that I should name the different versions of weighted pairwise so
that they can be distinguished from each other. How about "weighted
pairwise (cardinal ratings)" and "weighted pairwise (rating gaps)". For
those who like acronyms, so how about WP-CR and WP-RG?
	Anyway, I've been thinking about WP-RG, and it seems like it is quite a
bit more similar to AERLO and ATLO wv than WP-CR is. For example, let's
say that in WP-RG I vote 
A >0> B >0> C >10> D >10> E >0> F >0> G
	Isn't that extremely similar to voting A>B>C>D>E>F>G with an AERLO line
after C, and an ATLO line before E?
	That is, if there's no top cycle, then it doesn't matter. If there is a
top cycle, then my ballot does not count towards the following defeats if
they exist: A>B, A>C, B>C, E>F, E>G, F>G. In WP-RG it doesn't count
because, although the defeat exists, my ballot doesn't lend any ratings
weight to it. In AERLO/ATLO, my vote doesn't count because the preference
has become an equality on my ballot.
	Perhaps the only difference for this example is that in AERLO/ATLO, the
direction of a defeat can be changed as a result of AERLO/ATLO lines,
while this is not the case in either WP version. However, such flipped
defeats are likely to be rather weak anyway. Offhand I don't have any
examples where it would make a difference, although I guess if I sat down
for a while I could probably make one.
	So, I think that WP-RG can do a lot of what AERLO/ATLO can do, and as a
result of a similar process. The main difference, I think, is that you can
vote a set of preference gaps that are more complex than AERLO/ATLO can
allow. For example A >10> B >0> C >2> D >0> E... or whatever. Why exactly
would you want to vote that way? I don't really know. But I expect that
there would be some reason, in some situation or other. 
	The implementation argument between A/A and WP-RG is mixed. On the one
hand, the A/A ballot is a bit simpler, can exist with a more low-tech
interface. On the other hand, A/A is a bit more difficult to explain to
the average voter. Ratings gaps, while not as intuitive as cardinal
ratings by a mile, can at least make some immediate sense to voters. ("If
you prefer George to John, then, on a scale of 1 to 10, how much do you
prefer George to John?"... or whatever)
	Anyway, I guess that there are two very different branches of WP now.
Aesthetically, I still prefer WP-CR to WP-RG so far, but perhaps I'm just
being stubborn. I can see how WP-RG would be have the benefit of allowing
voters to vote as many preferences as they like at the maximum strength
even in the event of a cycle. On some level, though, I feel a bit more
comfortable finding the preference strength simply by subtracting ratings
rather than by identifying the largest ratings gap. 

	I guess that instead of simply choosing the largest gap you could also
have a version where you do add two smaller A>B and B>C gaps into a larger
A>C gap, but the added gap can't be more than the maximum (e.g. 10)... if
the sum of the gaps is more than 10, it's just counted as 10 anyway...
	But that seems messier still.

best,
James