But common purpose comes before > it's the choice. Self-interest is survival, which is secondary. After the choice. 
Take Care ^^
Self interest comes first, which should coincide with the common purpose.
A simple example: If I want to sell something, the other person must be interested to buy the same thing. It serves our self interest, but satisfies our common purpose - to get rich or to lead a better life. When this is combined with many buyers and sellers, there is unity.