I've seen this argument before, and it annoys me. In particular, to satisfy the second property, there is no need for a multiplication - simply assert the prope

I've seen this argument before, and it annoys me. In particular, to satisfy the second property, there is no need for a multiplication - simply assert the property. This yields the Mean Absolute Deviation error function, or E_1 in the article. To get variance, you need to be chiefly concerned with distributions that have a variance in the first place - and then the additional information contained in that statistic has an amount of descriptive power over that of the median.