In my experience MAD refers to either Median Absolute Deviation or the Mean Absolute Deviation. I was using the median version which is a pretty common "robust" statistic. Although I have occasionally seen the mean version it seems to be less common in practice.
Take a look at the Wikipedia you linked. No version of Average Absolute Deviation is consistent with Taleb's definition. No squaring, no square root. Sounds more like a geometric mean.
This is exactly what is so frustrating about Taleb. His ideas only partly makes sense. He often seems to see the problem but his solutions are poorly thought out. Of course, he thinks his solutions are perfect and everyone else is an idiot.
In what field do you work that the median absolute deviation is used at all, let alone more than the mean absolute deviation?
When he talked about mean absolute deviation being sqrt(pi/2) sigma did that not make it abundantly clear what he was discussing?
>No squaring, no square root. Sounds more like a geometric mean
Do you even know what the geometric mean is? (It has a root function so your statement just sounds stupid)
Dispersion functions are built off the distance function under the metric you want to use. Standard deviation uses the L2 metric, which implies a euclidean distance function. (L2 corresponds to summing pow(u-x,2) and pow(sum,-2) as your functions)
Mean absolute deviation takes the L1 metric, which implies pow(1) and pow(-1).
This becomes summing pow(abs(u-x),1) and then pow(sum,-1), which, needless to say is the same thing as averaging the absolute differences.
https://en.wikipedia.org/wiki/Median_absolute_deviation
Take a look at the Wikipedia you linked. No version of Average Absolute Deviation is consistent with Taleb's definition. No squaring, no square root. Sounds more like a geometric mean.
This is exactly what is so frustrating about Taleb. His ideas only partly makes sense. He often seems to see the problem but his solutions are poorly thought out. Of course, he thinks his solutions are perfect and everyone else is an idiot.