Since all economies are faced with scarcity, how might nations attempt to minimize the human hardship associated with scarcity?

Scarcity, utility and distribution are the underlying principles governing every economy. Human needs can never be satisfied (non-satiation principle) but the caveat is that when human attains more of the same things, they become happy (increasing utility: a measurement of satisfaction). However they do so at a decreasing measure (law of diminishing returns). This is where the principle of Pareto comes into play. It is only possible if best that could be achieved comes without disadvantaging at least one group.

Obviously, no nation can put into place policy instruments that can share the wealth of that nation equitably without disadvantaging somebody. In other words, Pareto principe cannot not be achieved in any nation. However, that does not negate the importance of this neo-classical theory, rather it provides government directions to distribute these scarce resource. This can only be achieved at sub-optimal conditions. remember also that there are what are referred to as public goods and private goods. Not everything come comes under government control (banking, informal sector etc.). In the same breath not evrything come under private control (water, rail/transport etc.).
In order to minimize hardships, good governments try to balance the control of these resources, determing which should fall into private hands and which it should control for the greater good of everybody (Socialism, capitalism, communism etc). These are all sub-optimal (ie they are not the best but acceptable under the prevailing circumstance). How well policy intstruments are used to determine the effect on the citizenry in reducing the hardship they find themselves.