Plato's ideal state, as described in his Republic, is ruled by philosopher-kings who possess the knowledge and virtue necessary to make just and wise decisions.

Aristotle believed that the state exists to enable individuals to live good and virtuous lives, and that its primary purpose is to promote their happiness.

According to social contract theorists such as Thomas Hobbes and John Locke, individuals give up some of their natural rights, such as the right to life and liberty, in exchange for the protection and benefits provided by the state.

John Locke's Two Treatises of Government argues that the legitimacy of a government depends on the consent of the governed, and that individuals have the right to rebel against a government that does not protect their natural rights.

Max Weber argued that legitimacy in modern societies is based on rational-legal authority, which is derived from a system of laws and institutions that are seen as legitimate by the majority of the population.

Amartya Sen argues that legitimacy is based on the ability of a government to deliver public goods and services effectively, and that governments that are able to improve the well-being of their citizens are more likely to be seen as legitimate.

One of the main challenges to political legitimacy in modern democracies is the decline of trust in government, which has been caused by a number of factors, including political scandals, economic crises, and the rise of social media.

Governments can increase their legitimacy in the eyes of their citizens by being more transparent and accountable, delivering public goods and services effectively, promoting economic growth and prosperity, and respecting human rights and civil liberties.

Political legitimacy and political stability are positively correlated, meaning that governments that are seen as legitimate are more likely to be stable and vice versa.

The French Revolution is often seen as a turning point in the development of political legitimacy because it challenged the traditional idea that legitimacy is based on divine right or tradition, and instead argued that legitimacy is based on the consent of the governed.

De jure legitimacy is based on the legal framework of a state, while de facto legitimacy is based on the actual support of the population for the government.

Thomas Hobbes argued that legitimacy is based on the ability of a government to maintain order and prevent chaos, and that individuals are willing to give up some of their freedoms in exchange for the protection provided by the state.

Jürgen Habermas argues that legitimacy is based on the ability of citizens to participate in political decision-making, and that governments that are able to create a public sphere in which citizens can freely and rationally debate political issues are more likely to be seen as legitimate.

Martha Nussbaum argues that legitimacy is based on the ability of a government to promote social justice and equality, and that governments that are able to create a society in which all citizens have equal opportunities and are able to live flourishing lives are more likely to be seen as legitimate.

As the world becomes increasingly interconnected and interdependent, the need for legitimate governments that can cooperate with each other and address global challenges will become more important.