In politics, authority generally refers to the ability to make laws, independent of the power to enforce them, or the ability to permit something. People obey authority out of respect, while they obey power out of fear. For example, "the congress has the authority to pass laws" vs "the police have the power to arrest law-breakers". Authority need not be consistent or rational, it only needs to be accepted as a source of permission or truth.
Questions as to who has what authority often lie at the heart of political debates, and answers to those questions normally stem from practical and moral considerations, from prior practices and from theories of criminal justice or of the just war.
In sociology, authority comprises a particular type of power. The dominant usage comes from functionalism and follows Weber in defining authority as power which is recognised as legitimate and justified by both the powerful and the powerless. Weber further sub-divided authority into three types:
Traditional authority which simply derives from long-established habits and social structures. The right of hereditary monarchs to rule furnishes an obvious example.
Charismatic authority. From time to time, people make extraordinary claims of heading a revolution of some kind (which is always against a well-established system of traditional or legal-rational authority). When followers take such claims seriously, this exemplifies charismatic authority: religious or political authority that does not flow from tradition or law, but instead thrives on the short-lived excitement of social change. The careers of Lenin, Martin Luther, Hitler, and Lech Walesa provide examples. Charismatic authority never lasts long (even when successful) and it inevitably gives way to either traditional or to legal-rational authority.
Legal-rational authority depends for its legitimacy on formal rules, usually written down, and often very complex. Modern societies depend on legal-rational authority.
As an example of the development of legal-rational authority, consider the history of France. In medieval times a king ruled simply because he was the king (i.e., he held traditional inherited authority), but by the 17th century it became necessary to invent a doctrine claiming that Louis XIV ruled by "divine right": in other words, to justify Louis' authority by a rational claim to his appointment by a legitimate superior (God). This served for another century, but was threatened by the rival claim made to legal-rational authority by the various legislative bodies of the early years of the French Revolution, and then eclipsed by the charismatic authority held by Robespierre and his cohort during the Reign of Terror, then the legal-rational authority of the Directory, and the mixed legal-rational and charismatic authority of the Consulate and First Republic (the charisma in this last case being that of Napoleon Bonaparte).
The Restoration (1814) marked a return to traditional authority, but now with elements of the legal-rational as well, at least until the ascent of Charles IX; his attempt to restore a more absolute monarchy brought on the July Revolution, which formally restored this balance of legal-rational and traditional in the form of a constitutional monarchy. The Revolution of 1848 passed rapidly into a legal-rational mode, falling ultimately to the Second Empire, which saw a blend of all three modes: the government Napoleon III retained a constitution of sorts and, in his person, he combined the Napoleonic charismatic claims with what was now a certain element of tradition, a Bonapartist dynasty to rival the Bourbons.
The complex pattern can be continued practically down to the present day, with a steadily diminishing role for traditional authority, except insofar as republicanism itself has become a tradition. In the Twentieth Century, France had at least two charismatic leaders, Philippe Pétain and Charles de Gaulle. The constitution of the Fifth Republic overtly a legal-rational system, was tailored specifically for the purpose of creating a presidency powerful enough that the charismatic leader de Gaulle would consent to accept it.
Within conflict theory, "authority" is used both in the same sense as Weber's functionalist definition above, and in a rather different sense which is based on the observation that power is almost never endorsed in a moral sense by those who do not have it, and therefore defines "authority" as power which is so institutionalised that it is largely unquestioned.
Obedience to authority seems thoroughly ingrained in most of the population: the Milgram experiment showed that over 60% of a sample of Americans demonstrated willingness to torture another person to death when given orders from an appropriate authority figure. This experiment produced similar results when replicated in several other cultures. A similar effect was found in the Stanford prison experiment.
An authority can also be a government agency set up with a particular competence and is able to deal with all matters within its charter; such as the Tennessee Valley Authority and a Port Authority. They are usually created by special legislation and are run by a board of directors. They are also, usually, required to be self-suppoting through property taxes or fees for services. See Special-purpose district.