[EM] Dyadic approval implemented as CR

[Roy]

Richard Moore wrote:
> Part of the appeal of the dyadic ballots is that they offer 
> more expressivity than mere rank voting. So you can not only 
> say that you like B better than C (B>C), you can say you 
> like B much, much better than C (B>>>C). But this binary 
> scoring method loses that advantage.

I'm sorry if I wasn't clear: my scoring method was intended to be 
identical to Dyadic Approval. The only change is to use CR balloting 
to express the preferences. It is possible, within CR, to say B is 
much, much better than C. Maybe I should give some examples:

A > B >> C > D

A and B both score 1 compared to C and D.
A scores 1/2 over B; C scores 1/2 over D.

The CR equivalent (on a 1-100 scale) would be
A 100 (or anywhere in the top quarter)
B 75  (or anywhere in the 2nd quarter)
C 25  (3rd quarter)
D 1   (4th quarter)

In general, in DA, the most >>>s indicate a 1 point advantage. A 
score is only given for the largest boundary crossed, so for example, 
A compared to D only gets credit for the >>, and nothing additional 
for the 2 single >s. For each > less than the maximum, the advantage 
is halved. If I've misunderstood how DA is scored, please let me know.

One more example, just for good measure:

A >>> B >> C > D

equates to:

A 100
B 50
C 25
D 0

A scores 1 over each of B, C, and D
B scores 1/2 over C and D
C scores 1/4 over D

>In fact, if we use summation, and I assume you mean "sum the rows", 

No, we sum the ballots (each ballot is a matrix) to get the matrix 
representing all the ballots. I was very brief in describing this 
because I'm not proposing any difference in scoring from DA.

> ... it seems like we haven't gained 
> anything over the Condorcet method with ordinary ranked 
> ballots. Am I missing something?

It is the coarseness of the scoring that gives DA its advantage. You 
can give A the maximum advantage over D without scoring them at the 
extreme ends. That gives you latitude to put things above and below A 
without changing the relative strength of A to D.