In an effort to understand political ideology, governance and voting patterns, many political scientists, observers and theorists have attempted to define politics in terms of spectra. A common way of referring to political positions is with reference to where they stand on a one-dimensional spectrum from left-to-right. Historically, this method of categorisation derives from the seating in the French Legislative Assembly of 1791, where the radical Montagnards sat on the left side of the chamber and the moderate Feuillants sat on the right.
Political spectrum theories that emphasise multiple axes or spectra have developed to avoid the shortcomings of the left-right divide. There are plenty of political actors who do not fall into simple spectrum theories. The British National Party is a populist, nativist, separatist party which are often described as "right-wing". Their economic policies have often been similar to that of left-wing parties like the (UK) Green Party - they support universal state-funded healthcare provision through the National Health System, with the proviso that it's only for racially native British citizens. It is not just within the fringes of politics that ideological complexity threatens simple left-right spectrum theories. On the British left, there has been a significant split between those who accept that governments may use military force to intervene in order to protect the democratic and civil rights of another country's citizens from a dictator, even in contravention of the dictates of the United Nations and other international regulations and bodies, and broadly anti-war left-wingers. This dispute can be seen as one where the domestic, economic and social policy of two groups - the so-called anti-war left and the so-called interventionist left - match but the foreign and military policy differ. The U.S. Republican Party has had a similarly uneasy relationship between the various factions within: while all members broadly accept the label "conservative" or even "right-wing", the relationship between the economic/business/'Wall Street'/'country club' Republicans and the more religious conservatives often becomes apparent.
In American politics, many libertarians do not adequately fit the traditional political spectrum. The American libertarian David Nolan has constructed a diagram that measures freedom on two axes - personal freedom and economic freedom. Those who support both personal and economic freedom are classed as libertarians. Those who support personal freedom but not economic freedom, are classed as left-liberals. Those who support economic freedoms but not personal freedoms are classed as right-conservative. Those who score low on both measures of freedom are classed as 'big government statists' (also labelled just statism, populism, authoritarianism, totalitarianism and communitarianism). More recent versions of the Nolan Chart, including the popular "World's Smallest Political Quiz" promoted by the Advocates for Self-Government, an American libertarian non-profit group. Some critics of libertarianism have argued that the "World's Smallest Political Quiz" is flawed in a number of ways: it is very small, containing only ten questions - five each for the two dimensions - some of which are broad and leading questions. The statement "Military service should be voluntary. There should be no draft." could be rewritten as "The military should not be allowed to draft soldiers, even in times of national emergency." and the level of support for the position would change dramatically.
The Political Compass uses the same dimensions as the Nolan/Advocates quiz, but with significantly more questions: instead of the ten used by the Advocates, the Political Compass uses 62 questions across six categories with four responses rather than three (Agree and Disagree, plus Strongly Agree and Strongly Disagree - Nolan/Advocates uses Yes, Maybe and No). Some of the questions map directly on to broadly European and American policy issues, but some also seek to identify the underlying moral, religious and ideological attitudes or 'worldview' positions which can be seen as just as important as the actual matters of policy when it comes to political identification and support for parties or candidates. The Political Compass has two axes - the Libertarian-Authoritarian axis and the Left-Right axis. The former maps onto the 'social freedom' score on the Nolan/Advocates schema, while the latter maps to 'economic freedom'. The four quadrants produced are labelled 'Libertarian Left' (a left-liberal in Nolan's chart), 'Libertarian Right' (Nolan's libertarians), 'Authoritarian Left' (Nolan's big government statists) and 'Authoritarian Right' (Nolan's right-conservatives). Political Compass provides a number of example graphs showing the relative placement of various parties and politicians including those running in recent elections in the United States, Canada, Britain, Ireland, Germany, Australia, New Zealand and the European Union elections.
Another similar two-dimensional ideological categorisation schema is that of the American writer Jerry Pournelle, constructed in his 1963 political science doctoral dissertation. The two axes on this model are labelled 'statism' and 'rationalism'. The 'statism' axis goes from 'state as ultimate evil' to 'state worship', while the 'rationalism' axis goes from 'irrationalism' to 'reason enthroned'. On this model, Communists and Libertarians/Objectivists (supporters of the ideology of Ayn Rand) both rank high on the 'rationalism' axis, even though in American politics, leftists who support welfare programs which tend towards a more socialist or communist ideology (in Pournelle's categories, state-worshipping rationalists) are naturally allied with classical anarchists and the "counterculture" movement, who are in the opposite quadrant (irrationalists who are skeptical of the state). A similar alliance is drawn in the other direction for the "right" of American politics - the libertarians and Objectivists (rational, state-skeptical) tend to be naturally allied with conservatives (state-worshipping irrationalists). Fascism and Nazism, according to Pournelle, are extreme forms of irrationalism tied to state-worship.
Related to issues of political spectrum, the horseshoe theory asserts that those on the far left of politics are closer to those on the far-right than they are to the political mainstream, and thus the linear spectrum can be thought of as being shaped more like the 'U'-shape of a horseshoe.
- See Mark Rupright's The World's Smallest Political Hook