Final answer:
Representative self-government in the English colonies developed through colonial legislative assemblies that had the power to legislate, control finances, and represent the electorate, leading to an expansion of their power and influence.
Step-by-step explanation:
Representative self-government developed in the English colonies primarily through colonial legislative assemblies. These assemblies had significant powers such as initiating legislation, controlling the budget by voting on taxes and expenditures, and petitioning the monarchy for redress of grievances. Importantly, the members of these assemblies were elected by the colonial populace with wider land ownership distribution leading to more men being able to vote compared to England.
Colonial legislatures and governors were often at odds with local elected bodies wielding the power of the purse to regulate the government. Over time, colonial assemblies steadily expanded their power and influence, shaping the development of self-government in accordance with the ideals of direct representation, unlike the British Parliament's system of virtual representation.