The seventeenth and eighteenth century philosophers john locke, jean jacques rousseau and thomas hobbes supported which theory of government

The answer is "social contract theory".

It is the willful understanding among people by which, as per any of different speculations, as of Hobbes, Locke, or Rousseau, sorted out society is carried into being and contributed with the privilege to anchor shared security and welfare or to direct the relations among its individuals.

 SOCIAL CONTRACT theory

Explanation:

In modern political theory, Thomas Hobbes was the first to point to the social contract as the source of a government's authority.  His argument still supported a strong monarch style of government for the sake of a country's security and stability -- whoever was put in charge of government needed to have absolute power.  But Hobbes was asserting that a government's power came from the people, not something granted from God (as was previously thought). Thomas Hobbes published his political theory in Leviathan  in 1651, following the chaos and destruction of the English Civil War.  He saw human beings as naturally suspicious of one another, in competition with each other, and evil toward one another as a result.  Forming a government meant giving up personal liberty, but gaining security against what would otherwise be a situation of every person at war with every other person.

Later Enlightenment philosophers such as John Locke and Jean-Jacques Rousseau expanded on the social contract theory and gave the people an ongoing role of sovereignty, rather than seeing the ruler as the sovereign once he was in power.

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