'each society' is correct and usable in written English.
You can use it in a sentence to describe a group of societies or cultures. For example, "Each society has its own unique set of beliefs and customs."
Deciding how the costs should be shared is a matter for each society to judge.
What of men born in 1957, 1970 , 1983-- each society more degenerate and confused?
Each society must search for its own path, and no path is perfect.
Over the following weeks, each society will march at its neighbours' events.
Each society must find the proper balance for allocating benefits among labor, consumers, management and shareholders.
The enemy has built a wall right up against their city wall; each society refuses to see the other.
Spending time in jail is no fun anywhere, but each society has its own cultural refinements of misery.
The real test would be to take babies from each society and bring them up in the other.
Each society had its own political paradigms, and found it difficult to understand – let alone respect – alien political concepts.
The imaginations of general public toward the futures are given in each society by using these analogies: railroad, river, sea and game.
In fact, civilizations are hard to partition in this way, given the diversities within each society as well as the linkages among different countries and cultures.
