The definition of Pareto efficient is along the lines of "a
state in which the conditions for some can not be
improved without worsening the conditions of others."
Note that a Pareto efficient or Pareto optimal state is not nesesarily an objectively good state. However, any state that is NOT Pareto efficient is not a good state. For instance given the three states
A1: {11, 5, 5, 5}
A2: {11, 6, 5, 5}
A3: {10, 11, 11, 11}
Here, A2 and A3 are Pareto efficient, while A1 is
Pareto deficient. If we are in state A1, we can go to A2, thus increasing
happiness (or
whatever we are measuring) for the second and third persons without causing harm to anybody else. However, while A3 maximises the sum and would therefore appear to be objectively better than A1 and A2, the first person would prefer A1 or A2 instead.
So, state A1 is unpreferable, since it is not Pareto optimal. Anybody who claims that A1 is an optimal configuration given some qualities of measurement is wrong! However, what is best of A2 and A3 all depends on the context and on the oppinions of those who decide. Another example
A1: {100, 50, 50, 50}
A2: { 50, 50, 50, 50}
While A2 may appear '
fairer' that A1 because the difference between the maximum and the minimum is 0, it is actually Pareto deficient. Nobody looses by going from A2 to A1. This describes why an
even distribution of wealth is not a very good measurement for the quality of an
economy.