|Oh no, they're talking about|
Political spectrums are heuristic representations of different political ideologies and how they relate to one another. It can function as a useful tool for understanding how different ideas, parties and people compare and differ but, like all heuristics, it is an over-simplification and one should be careful not to mistake the map for the territory.
The one dimensional model
At its most basic, the political spectrum consists of a continuum from left to right, with varying shades of opinion in between. The terms "left-wing" and "right-wing" originated in the years following the French Revolution of 1789. The nobility was seated on the right side of the 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 demands progress and equality however, in most well-established liberal democracies, what used to be left-wing (support for free-markets and the maximising of personal liberty) is now more associated with libertarianism who accordingly often dub themselves "classical liberals" to differentiate themselves from more progessive liberals and social democrats who are more obviously on the left and may support things like the welfare state or affirmative action.
Typically this model that spreads political affiliations across one dimension has anarchists, communists and socialists bunched up on one end, fascists and neo-nazis on the other and beleagured centrists in the middle. Significantly more nuanced ways of assembling a political spectrum exist but the single dimensional spectrum from "left" to "right" is the most commonly used in punditry and political discourse.
Problems with a one dimensional model
There are a number of problems with this model. One is that it flattens differences between a number very different political schools of thought. For example, it treats stalinists and anarchists as near identical. Another is the treatment of political difference as though it were a quantitive question. While social democrats and marxists might propose similar policies now and again they have very qualitatively different views from one-another with the former being pro-capitalism and the latter ultimately seeking its abolishment. These two groups don't disagree about what percentage of capitalism should happen but rather whether capitalism should happen at all but this difference is difficult to communicate using any kind of quantative spectrum.
And it's not just the political left that has an issue with the conventional one dimensional spectrum. Libertarians who believe in bodily autonomy and are pro-choice, pro-legalisation of drugs, sceptical of the police and anti-war can find themselves forced to rub shoulders with anti-abortion, pro-war on drugs, cop-loving, war-hawks which many of them resent.
Then there is also the issue of green politics, which have been espoused by people on practically every point on the left-right political axis, from the far-left saying that capitalism doesn't work because we are polluting our planet to the far-right arguing that some races pollute more than others, passing through moderates who use environmentalism as an argument for economic planning. The large scale of people using environmentalism to justify their means makes it practically impossible for these politics to be classified under this spectrum.
The two dimensional models
Some 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. However, the theoretical merit of a two-dimensional political compass is a separate issue from its actual implementation in practice. Given that the actual political compass website classifies Bernie Sanders as a centrist, its accuracy is questionable.
Two dimensional models like the political compass and the nolan chart are however, a marked improvement on the one-dimensional model. At the very least they are capable of distinguishing neo-nazi's from libertarians and DPRK supporters from libertarian socialists.
Problems with the two dimensional models
While we can now make more satisfactory distinctions between liberals and libertarians there are still ways in which these spectrums mislead us and misconstrue the nature of political difference.
Under these models both anarchists and right wing libertarians are described as "libertarian" despite the fact that they have very different ideas about what that word means. Anarchists tend to support a more positive form of liberty that includes rights to things like food, medical care, education and participation in decision making. For right-wing libertarians, their conception of liberty is more "negative" and is primarily a freedom from external interference. Right wing libertarians typically do not believe that you have a right to food, medical care, education or participation in decision making at your place of work. Yet despite these massive conflicts in their desired outcomes, intended policies and contradictory understandings of what the word liberty entails both the nolan chart and the political compass understand both these movements as "libertarian"... which skips over a lot of important distinctions.
Another problem that should be considered is the way in which these models position "authoritarianism" as though it were a value that is actively endorsed. For marxist lenninists (who typically score as authoritarians) quickly crushing the opposition is important to defeat the forces of reaction who may be just as or even more tyrannical. Anarchists (who typically score as libertarians) during the Spanish civil war also imprisoned political opponents, established labour camps, engaged in terrorism and summary execution: actions which are often defended across much the same lines that they were necessary to prevent fascists from getting the upper-hand. In these cases similar measures and methods are endorsed in practise but because marxist lenninists are typically more open about what their revolution will involve they get classed as "authoritarian", where-as the anarchists don't. The difference being not so much in what each group values but in what they are willing to admit.
It is also worth noting that terms like "economic freedom" could be considered politically weighted. Leftists might refer to it as "corporate authority" instead.
Extremism & Horseshoe Theory
Extremism is a catch-all term for those whose political or religious views are far from the center of a given political spectrum, with connotations of being dangerously so. It is often synonymous with "wingnut" and/or "moonbat" (both being similar weasel words).
Horseshoe theory is an idea popular among the dimmer minds of the centrists which argues that ultimately the "far left" and "far right" are identical; contorting the one-dimensional spectrum into a horseshoe shape. This kind of spectrum ultimately compounds the problems the regular one dimensional spectrum has by lumping far-left anarchists not just in with stalinists but also reactionary incels and neo-nazis as well.
Such a theory, which posits that "mild mannered centrism" is the ultimate antidote to authoritarianism, also fails to note or explain the occasions in which free-market orientated liberal democracies (which centrists tend to support) have abused human rights and used authoritarian means to achieve their aims.[note 1]
- While Centrists may argue that they don't consider such governments or actors to really be reflective of the 'centrist ethos' such a defence fails as it is a No True Scotsman fallacy.