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The political spectrum is a concept for representing different political stances in relation to one another.
At its most basic, the political spectrum consists of a line or continuum from left to right, with varying shades of opinion in between. Some people, particularly those at the far sides of the spectrum, will tend to simplify it futher to be just two positions; left or right, with no room for compromise. More realistic ways of assembling a political spectrum tend to be far more complex, but the single dimensional spectrum from "left" to "right" is the most commonly used and most popular.
 The left-right axis
The terms "left-wing" and "right-wing" originated in the years following the French Revolution of 1789, when the nobility were seated on the right side in parliament meeting, and representatives of the liberal bourgeoisie sat on the left. Thus, the term "right-wing" became associated with maintaining the status quo and protecting the interests of the established elites, like the nobility, clergy and the wealthy. The "left-wing" is associated with demanding progress and equality, although the extent can vary from liberals who seek change through economic reform (while retaining a market-based system) to socialists, who advocate the destruction of capitalism and collective ownership of the means of production.
The following is the classic left-to-right political spectrum that still makes a good deal of sense to many people in the United States of America and resonates strongly throughout Western civilizations. Included in this basic linear political spectrum are examples of western ideologies and where they would fit:
 Understanding this left-to-right political spectrum
There are several problems with the the left-to-right spectrum. One is that the uses and definitions of the terms vary considerably between different cultures and contexts, since they are dependent on the political and economic status quo. For example, in authoritarian countries such as the USSR or China, hard-liners have sometimes been described as "conservatives," while proponents of the free market were regarded as progressive reformers, essentially the opposite of how the left and right wings of a spectrum would be labelled in democratic countries. "Centrism" is not so much a clearly distinguishable position in its own right, as it is always defined in the context of other positions - what counts as a "centrist" position in one country may well be considered extreme in another. The terms "left" and "right" are also meaningless for people in many non-Western cultures, simply because they lack a tradition of categorizing politicians and parties in this manner. Another problem with the left-right distinction is that it suggests a one-dimensional spectrum that is often reduced to disagreements over economic policy, ignoring the importance of social issues and freedoms.
Another common observation is that the movements found at both the far-left and far-right positions tend to have more in common with each other than they do with more moderate liberals or conservatives, since both extremes have a tendency towards radicalism and totalitarianism. The horseshoe theory contends that the left-right axis should be viewed in terms of a horseshoe curve, with the ends of the axis curving towards each other, rather than a straight line from one extreme to the other.
 "Leftism" and "rightism"
Although the meanings of left and right vary between different countries, there is more than sufficient shared meaning to enable leftists in one country to affiliate with leftists in other countries and for rightists in in one country to affiliate with rightists in other countries, unless of course their countries are at war. The shared meanings that form the bases for their affiliation involve beliefs about human nature. Otherwise, they would be unable to form organizations like the Socialist International or the International Democrat Union.
Despite the "-ism," these labels do not designate a distinctive position that has at least some form of a common ideological and philosophical base, but are most often used to label people as having veered outside of the mainstream and towards one of the fringes of the spectrum. "Leftist" is widely used in US politics to refer to socialism and anti-capitalist ideologies, although it is also often mistakenly applied to liberals, which can cause confusion and resentment, since there is a vast difference between the two groups. For anyone who studies politics with rigor, the conflation of "leftist" and "liberal" is truly infuriating; the American right-wing talking point machine refers to anyone "left of center-right" (e.g. Hillary Clinton, Al Franken), as a "far-left" politician or pundit, further confusing political discourse. Indeed, the nomenclature of US politics is so skewed as to be practically unrecognizable to anyone from outside the US.
Some leftists wish to overthrow capitalism, and believe that "bourgeois democracy" is a sham, designed only to keep the rich in their places of privilege, while others believe in achieving a socialist society through democratic means. There are many different forms of leftism, as reflected in such terms as Marxist, Marxist-Leninist, Stalinist, Trotskyite neo-Trostkyite, Maoist, democratic socialist, libertarian socialist, anarchist, De Leonist, council communist, guild socialist, etc., not to mention various modern and postmodern theoretical schools that seem to exist mainly in academic circles, such as deconstructionism, left- or post-feminism, Critical Theory, and the Frankfurt School. Many of these groups have a fierce rivalry with each other, such as the Marxist-Leninists with libertarian socialists, and the Stalinists and Maoists with just about everybody else.
The term rightism is rarely used, but tends to refer to a form of extreme conservatism that seeks to do away with democratic politics entirely. In the past, most "rightist" groups either sought a restoration of a previous monarchy, or the creation of a fascist or authoritarian regime to "undo the chaos of democracy." Because the United States has never had a monarch or a totalitarian movement, "true" rightist groups in that country have been relatively few, though the US government has helped fascists such as Pinochet come into power. Another common component of rightism, however, has not waned: extreme nationalism. Most rightist groups try to force out all immigrants and minorities. It is possible that in modern rightism this form of nationalism is the only defining characteristic.
 Other measures
Another problem with the left-to-right spectrum is that there are some political positions which do not fit into it. For example, libertarianism upholds both personal liberties (traditionally left-wing) and unrestrained economic freedom (traditionally right-wing). This hasn't stopped some libertarians from claiming that therefore they are centrists.
Libertarians often contend that a full variety of opinions can be better represented by two-dimensional diagrams where the (economic) left-to-right spectrum is balanced with another (social) axis representing a varying level of restriction on civil and social freedoms, both of which can be either left and right wing. Two examples of such a representation are the Nolan Chart and the Political Compass, where political opinions can be plotted anywhere in a square grid based on the two axes.
The Vosem chart reworks the Nolan chart into three axes: Cultural, fiscal, and corporate. The two ends of each axis are sometimes labeled as "hierarchical" vs. "egalitarian."