The Massachusetts Bay Colony operated as a representative theocracy. Government officials were elected, but the electorate was made completely comprised of Puritans.
The Massachusetts Bay Colony was founded by English Puritans who formed a company, known as the Massachusetts Bay Company, in England with the purpose of creating a colony for likeminded men and women in North America. As a company, they received a charter from the King of England, which they wisely carried to the colony with them. This afforded the leaders of the Company, all of whom migrated to Massachusetts Bay, a great deal of autonomy, and the charter served as the founding document for the colony. Thus the Massachusetts Bay Colony became a commonwealth or a republic, with Puritan church members (men) electing the colony's governor and other officials. John Winthrop, the leader of the Company, emerged as a political leader as well, serving as governor multiple times. At the local level, full church members could actively participate in electing ministers and participating in town meetings. As each Puritan town was responsible for establishing and supporting a church, this in effect made government at the local level quite democratic, at least for church members, the so-called "saints" who received full membership. So the political system of the Massachusetts Bay Colony was, essentially, what has been called a "Bible Commonwealth" that conferred considerable political power on church members.