The Social Contract states that the only legitimate right to govern comes from a mandate of the people. It was written by Jean-Jacques Rousseau and greatly influenced the American Founding Fathers.

John Locke is often considered the grandfather of the American constitution. His ideas on natural rights of life, liberty, and property and limited government are ideas that inspired the Founders. Other philosophers in the question came later, and were not specifically tied to early constitutional framers.

John Locke wrote that man was endowed with the natural rights of life, liberty, and property. Thomas Jefferson changed it to Pursuit of Happiness when he wrote the Declaration of Independence.

The American system is often described as a democracy, but a more technical definition is a representative republic, where the people elect representatives to reflect their interests in a congress. A true democracy is when citizens have direct voting power, as in some Ancient Greek city-state governments.

Based on the philosophy of John Locke, a social contract is an agreement between society and government about how subjects are to be ruled. The social contract according to Locke was that government ruled at the behest of the people and its primary purpose was to protect natural rights.

John Locke is the correct answer. This was not a tricky question, it, [un]fortunately just requires rote memorization. Remember: popular sovereignty means that we the people elect representatives to rule for us, and they rule with our consent.

The other political philosophers can all be found in the constitution (not their names, of course, but their political ideas):

Isaac Newton: Action/reaction—checks and balances

Montesquieu: separation of powers between a legislature, executive, and judiciary

Hume: pluralism

Hobbes: elements of social contract theory 

Baron de Montesquieu penned the idea of separation of powers in a political treatise. The Founders, to a large extent, followed his model—an executive, legislature, and a judiciary, each independent of one another. This was a fairly novel approach. Take Britain, for example. Britain has a unitary system of government (a constitutional monarchy, in fact), whereby nearly all of the power is concentrated in the legislature. The British legislature, “Parliament,” is bicameral, consisting of an upper (House of Lords) and lower (House of Commons) chamber. The executive is called the Prime Minister (PM), and comes from the legislature itself. What’s more, the PM is beholden to the legislature—in other, oversimplified, words, the PM is subject to the legislature. Until quite recently, the highest court was technically part of the legislature as well—the House of Lords consisted of “Law Lords” which interpreted the law.

Our government, however, operates completely differently. Other than impeachment, the President is not accountable to the legislature; he is beholden to the voters (technically the Electoral College). Similarly, other than being confirmed by the Senate, the Supreme Court is separate from the legislature.  Thus, the Founders completely broke with British tradition and created the Constitution [in part] based on Montesquieu’s theory of separation of power.

The three elements of Constitutionalism are limited government, rule of law, and the fundamental worth of each individual. The framers believed that a government limited in power would be more responsible for its actions. The rule of law declares the Constitution "the supreme law of the land" or "higher law," meaning that no one or no other law is above the Constitution. Everyone is held accountable to the same standards outlined in the Constitution. The fundamental rights of each individual are most obviously observed in the Bill of Rights. This concept guarantees rights and liberties to each individual.  

Anti-federalists strongly supported power to the states and the bill of rights. Anti-federalists were strongly opposed to the idea of a centralized, powerful authority figure. Rather, they wanted power to be left in the states. As a result, they supported a small national government that would be more responsive to the people. For these reasons, anti-federalists did not support the adoption of the Constitution. The anti-federalists also wanted a Bill of Rights to ensure their liberties without government interference. Upon adopting the Constitution, a Bill of Rights was added as a compromise.

The Individualism theory of politics supports a procedural view of justice. A procedural view of justice states that a political system is only legitimate as long as it applies fair rules and procedures equally to all people. The Communitarian theory, on the other hand, supports a substantative view of justice. This means that justice is obtained through fairness of obtained results (fair procedures are not a measure of justice, but rather the results of procedures).