Consider the replacement of square in QIM with the log function. This equality metric is useful in modeling realistic expectations.

When I compare the inequality of my networth with those very rich people, I am actually not very hurt by that fact. They are distant to me and I could care less if they owned a moon, as long as they don’t drop it on me, I’m fine with it.

But if you compare your networth with those of my college freshman classmates, or those of graduate school classmates, of with those of my coworkers, then suddenly, even a difference of \$100 could put me in very bad mood. The underlying cause of my bias is unknown to me. But if my feeling were a guide to what is truly unequal, I am able to write it, approximately, as

$log(a-b)$

It is quite noticeable that this curve, for the LIM, has very different shape than the QIM. But perhaps because my k-nearest-neighbors occupy more attainable positions. It is likely that I can get an equally large size of cow guts as the señor at the next table. It is unlikely that I can wrestle Micro\$oft to the mat by writing a new operating system. In fact one could almost imagine

$(a-b)^{-1}$

With the infinity at complete equality set to zero. The Inverse Inequality Metric (IIM), along with its partner the LIM can perhaps be most useful in personal servicee effort to gain equality. For example, I can try smiling a bit more at the cashier and waitress in my neighborhood restaurant while I order cow tounge in Spanish. A little respect will impact my $C$ little, while it may lead to increased $E$ and consequently a larger piece of the cow($dX$).