# Differential Efficiency of Servicing

A common meta-criterion applied to metrics such as QIM is to compute difference and rates. Instead of measuring absolute utility: my eating of cow guts lands me in a state of X satisfaction, we would measure the change in such metric due to servicing cow guts to me.

$X_{beforecowguts} -X_{aftercowguts}$

This creates a differential measurement of my utility due to experiencing said service. For simplicity, this can be written as

$dX_{cowguts}$

Another obvious heuristic often applied to measurement of utility due to effort is the rate of return, such as ROI. Since the service is performed at a measurable cost to both the servicer and servicee, we can compute two efficiencies. Let’s name the effort that provider makes in providing the service to me as $E$ and the cost to me, the servicee, as $C$. Therefore we have two new metrics

${dX}\over{C}$

Which directly measures return on my investment in patronizing the service. A second measure, in case above metric is unsatisfied, that we can check

$E\over{C}$

To see if the servicer is making a real effort to provide the service.

(Some handwaving is made here as to dimensional analysis. Let’s assume for simplicity sake that all benefits, efforts and costs are denomable in USD. But one can imagine some supernatural Karmic measurement that is even more universal than USD be used in this computation. As long as said unit obeys a basic set of algebraic laws some where above a semi-group. Also, it seems tolerable for benefit to have different units than effort and cost)

QIM ensues normally after this point.

These derivations and suggestions are not necessarily, as yet, grounded in any moral ideals. There is no assumption of inalienable rights, or supernaturally endowed rights. There is no insistence that the service impact each servicee the same or to bring their utility on-par with anyone else experiencing the service. The metric admits failure to measure unequal opportunities, at least in it’s original form. These ideas come to mind intuitively and their measurement are not universal. Since the formulas are not based on any declared axioms, I can only suggest that it be a standardized mechanism to be used in governmental policies to declare requirements of equality where that is desired. Another application, when desirable, one might use QIM on differential efficiency of service as a differentiable auxilary penalty to main objective function of deep neural networks and other machine learning algorithms. Furthermore, said method is only heuristically discriminative at best–it does not prescribe how to provide the service, all it can do is detect inequalities , and a few causes there of, in the providing and receiving of a service. That is to say, there is no guarantee that: 1) $G$od approves, or 2) It provides for maximization of total utility and 3) it cannot inform directly regarding performance of fairly equal service.

Okay, so much for disclaimers, let’s try to move on to something more interesting…