Final answer:
Classical Liberalism is the political ideology that promotes limited government and individual liberties, in contrast to anarchism which rejects the state entirely. It endorses capitalism and private property, with advocates like John Stuart Mill championing personal freedom within the bounds of not harming others.
Step-by-step explanation:
The political ideology that emphasizes limited government authority and individual liberties, contrasting with anarchists who reject the state entirely, is a) Classical Liberalism. Classical liberalism is built on the foundation of protecting natural rights and fostering an environment where individuals can act freely without undue government intervention. This ideology supports a capitalist economy, where private property and market trade are considered essential for prosperity and individual fulfillment.Advocates of classical liberalism, such as John Stuart Mill, argued for personal freedom that extends to all activities that do not cause harm to others, and although some liberal thinkers called for more governmental regulation during times of economic crisis, staunch classical liberals like Hayek opposed such measures, defending the merits of minimal state interference in economic affairs. Furthermore, classical liberalism distinguishes itself from libertarianism by traditionally advocating some level of government involvement to guarantee individual rights, in contrast to strict libertarianism's call for an even more reduced government role.