The pilgrims wrote it all together. It is unknown who literally wrote the document. They wrote it in 1620. The picture represents someone signing the paper while the other pilgrims watched.
They wrote the Mayflower Compact so they could have a government and enforce laws. They wanted to make sure people weren't just doing whatever they wanted. The picture states what would most likely happen if they had no government.
The document let the pilgrims have governments so they could now enforce laws. It changed because now everyone could have rules to follow and live their life in harmony.