Warren Smith wrote:
All your other knobs are input knobs, no? The #candidates, #winners,
utility generation models and parameters, etc., specify what kind of
data is run through the voting methods (and subsequent utility
determination function), whereas the weight-knob is an adjustment of the
(combined) utility function itself.
So it would seem to be a quite different sort of knob. Adjusting it
would be similar to adjusting 1-stage BR between, say, mean utility and
worst utility (maximin).
--I don't agree that it is a "different" kind of knob. It's just another knob.
Your claim the others are "input" knobs is an arbitrary judgment by you, and
I can regard at least some of them as "not input" equally validly/arbitrarily.
Are you claiming that the separation into input/not-input (as opposed to
some other divide) is arbitrary, or that my labeling of the weighting as
output rather than input is arbitrary?
If it is the latter, I would disagree. Input is that which, when
changed, changes what is supplied to the voting methods under test.
Output is that which could be adjusted even if the voting methods were
run only once: i.e. parameters regarding how to interpret the results
from the voting methods themselves, with respect to the utility data
already supplied.
Or in other words: if you give me only the utility data and the output
from the voting methods, for each round, I can calculate the results for
many different output knob settings, but not input knob settings.
I also don't agree that maximin utility should be of interest.
The comparison did not, as a comparison, regard whether maximin should
be of interest or not, but rather attempted to show the category
division in another manner. If I have the round results (and utility
data) for each round, I can find both mean and maximin utility (and
median, interquartile, you name it), but I can't simulate the results
for another number of candidates (unless I clone some of the candidates,
for instance).
In the more indirect sense, you might claim that if you don't agree that
maximin utility should be of interest, there's no need to introduce it
as a knob in the first place. What the comparison said, though, was that
if others disagreed, then the question of what weight to choose (between
mean and maximin, or just all-one and none of the other) would be
similar to the question of what weight to choose between 1-stage and
2-stage BR, and the same arguments for (e.g.) doing a 2D diagram rather
than just a weighted combination, would apply.
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