CR pairwise

[Richard Moore]

Roy One wrote:
 > See my posting "Dyadic approval implented as CR" for my 
suggestion
 > for addressing this. See also Richard Moore's comments 
about weak
 > information obscuring strategy in that thread.

Well, I hate to say it but I'm not sure if I was right about
that. I may have been looking for more utility (pardon the
pun) in CR than is really there. It's not really clear to me
if having weak information doesn't merely put you back into
the zero-info scenario, in which case the optimum strategy
is *still* to vote full-scale up or down for all candidates.
For example, you like Alice>Bob>Carol>David>Ed, and you have
just enough information to vote Alice and Bob up, and David
and Ed down. Maybe you know that Bob and David are the most
likely winners, and Alice and Ed can be ignored as long
shots. You don't know enough to decide what to do with
Carol; i.e., you don't know if Bob or David is more likely
to win. So does it make sense to vote your sincere CR for
Carol (or some slighly skewed version of that rating
depending on the circumstances), or does it make more sense
to treat it as you would a ZI election between Bob, Carol,
and David? If it's the latter then you would vote Carol all
the way up if her utility is higher than the average of
Bob's and David's, else you vote her all the way down.

I'm still a bit ambiguous about the philosophy behind this.
We can calculate the expected value of our vote as the dot 
product of our ballot and the strategic value (which in turn 
is the product of a delta-P matrix and our candidate utility 
vector). If we have a complete set of delta-Ps and a 
complete set of candidate utilities we can always figure out 
what our optimum ballot is. We would only vote sincerely in 
CR if we can't find an optimum ballot. If we can't optimize 
our ballot it means that some of the values are unknown (the 
matrix has blank cells). But is it really legitimate to 
leave those entries blank? It seems like the  delta-Ps *do* 
exist whether we know what they are or not (see note below), 
so leaving them blank doesn't seem right. Plugging in 
made-up values somehow seems strange, too. But that's what 
we do in true ZI cases: We assume all delta-Ps that aren't 
on the diagonal are equal and negative, and fill in the 
diagonal with the positive numbers that make the row sums 
equal to zero. In "true" ZI this doesn't seem odd in the 
least, so why should it seem like an odd thing in the 
weak-information (WI) case? It's not odd in ZI because 
whatever the "real" probabilities are, the best we can do 
strategically is to use delta-Ps that are a function of the 
information available to us, and with no information 
whatsoever the function yields the same result for each 
candidate pair. I am led to believe a similar argument would 
apply to WI cases, but are there exceptions?

Does anyone else out there have any thoughts on this?

Richard


(Note) This raises another philosophical question. Do 
probabilities exist for a unique event? If so, how can they 
be determined, and how do we validate the probability we 
arrive at? The best answer I can come up with at the moment 
is this: We cannot validate our estimated probability for a 
one-time event, but if that probability was generated by a 
model, and the model can be applied to other (equally 
unique) events of the same class, we can validate the model. 
An example would be the Keilis-Borok model for predicting 
whether the next US Presidential election will be won by the 
incumbent or the (major party) challenger: You couldn't 
legitimately validate the model's prediction for a 
particular election, but you can validate the *model* by 
observing how well it predicts a series of elections. 
Predicting the weather is another example: If the weatherman 
says the chance of rain is 60%, and it doesn't rain, was it 
a bad prediction? You can't say, but if you observe long 
enough you can say whether the model he is using is a good one.