This story is repeated endlessly at Thanksgiving and is not accurate. The pilgrims did not institute socialism in their new colony, but the common ownership terms were forced upon them by the stocking holding company which financed their colony. Their agent agreed to the terms without telling them and they found out as they were boarding the ships to the new world. It took a number of years to prove to the company that the system was not workable. Once they did, it took another decade to pay off their debt to the company.
Read: PURITAN ECONOMIC EXPERIMENTS BY Gary North (his PhD dissertation)
or this article from the Freeman by the same author: