What is the process by which a society decides how power and resources will be distributed within that society?

If it is on a gloabal scale then the factor would be: supply and demand.I have this product, you want this product, i sell this product to you for 'fair' market value(in a perfect world) or trade it for other commodities.

If you are speaking about a 'commune' style utopia-then the wealth/commodity/product is shared by all equally(communism)after it is gained/farmed/made by the commune...equally.