Arguments around measures of efficiency.

Of all the efficiency principals Pareto efficiency and Pareto superiority are widely known. At times Pareto efficiency is even used as the definition of efficiency.
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Mathematically,

In two different states $s_1$ and $s_2$, $s_1$ is said to be Pareto superior than $s_2$ if and only if following holds.
$u_i(s_1) \geq u_i(s_2)$ with strict inequality for atleast one individual.

State $s_1$ is said to be pareto optimal if there exists no state $s^*$ such that aleast for one individual $j$, $u_j(s^*) > u_j(s)$ and $u_i(s^*) \geq u_i(s_1)$ for the rest.


One of the other notions of efficiency is Hicks-Kaldor efficiency.
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Mathematically,
for two states $s_1$ and $s_2$ if
for $sum_{i \in N}u_i$
$\sum_{i=1}^(N) u_i$
$$sum_{i \in N}$$
for suitable compensation $d_i \in D=$

The issue with such an aggregative efficient notion is two-fold.
First, how do we come up with such aggregation, from individuals to system as a whole?
Secondly, Why and how would individuals continue to do so?
Hicks-Kaldor efficiency does away with the second issue as it divorces the concept of efficiency from that of moral well being. While assuming provision of "fair" compensation. Compensating affected individuals as such to keep them at a certain level of well-being is not necessarily morally correct, for it increases inequality at a new state.