i.e. low * low = low
high * low = < low
high * high = high
not the same with averaging
((low+high)/2) > low
where as with factoring is (low x high) is still < low.
All relevant posts you've already read.
I don't know how to explain it any better than the red/green graph that is drawn to show the difference between splitting around a median value from good vs bad values.
The green/red graph showed what would happen in a flat distribution of say 2 aspects (from 1 to 100%) either averaged together vs factored together, then the data is split between good/bad values around their median (green/red).
I guess since it's a standard approach to quantifying multiple aspects... the idea whether it's good or not is already addressed... now the merits of weighted average vs weighted product would be in order
I'll look at the geometric mean. I remember reading about that a while back and didn't know what one could use it for.
Update
I think I can solve the issue with weighted products losing their relative distance by not using it entirely, but doing a weighted average between a weighted average and a weighted product who's distribution curve has been flattened using an empirical cumulative distribution function.. Sorry for the nerd talk, but any dataset can be "flattened" i.e. converted to a flat distribution by deriving it's empirical cumulative distribution function, something that is kinda done for preferences atm.
Update 2
I think I get what I'm doing wrong
sumOfWeights = sum of Attribute weights
( A*AspectWeight1 / B * AspectWeight2/ C * AspectWeight1) ^ ((product of aspectWeights)/sumOfGlobalWeights)
= weighted product vs
weighted averaged
(AspectWeight1 +AspectWeight2 +CAspectWeight3)/(sumOfAspectWeights)
I also figured out how to do the geo mean
say
n = # of elements
elements =
a, b, c
(a*b*c)^1/n
A geometric mean is interesting... It might cut down a lot of the work that has already been done.
The goal was to derive a 50% point amongst attributes first. The only way I could get a good 50% point at ~ mean or median was to double transform around them. If a "geometric" mean, which may be better than a trimean... gives me a better 50% point... god be praised
oh wait... *shister* it is, or seems to be.
1, 2, 3 ,4
geomean is
0.499840136
that's the highest damn number I've seen close to .5 when I transformed around it
wait, I didn't account for min... anyways, I'll check into it.