Political spectrum

A political spectrum is a way of comparing or visualizing different political positions. It does this by placing them upon one or more geometric axes symbolising political dimensions that it models as being independent of one another.

Many editors of electowiki prefer to think of the political spectrum as a multi-dimensional entity. Few editors agree on the best abstract definition of this spectrum.

Formal definition
Mathematically, a political spectrum is defined by:


 * a dimension n, representing the number of independent issues under consideration. Voters are represented by points in V = [0,1]n.
 * a voter density function v: V &rarr; &real;
 * a distance function d: V &times; V &rarr; &real; that is positive definite and symmetric and satisfies the triangle inequality. Ballots are determined from the assumption that voters prefer candidates which are closer (according to this distance function) to them.

Ultimately, these are projections of a multi-dimensional political space onto a space of fewer dimensions, to generalize and make discussion simpler.

One-dimensional
A single-dimensional model envisions a horizontal line, with voters distributed along a single left-to-right axis. This is frequently referred to as the left–right political spectrum, and is how many people classify political positions, ideologies and parties. The people on the ends are said to practice extremism, and the intermediate stance is called centrism. On this type of political spectrum, left-wing politics and right-wing politics are often presented as opposed, although a particular individual or group may take a left-wing stance on one matter and a right-wing stance on another; and some stances may overlap and be considered either left-wing or right-wing depending on the ideology. In France, where the terms originated, the left has been called "the party of movement" and the right "the party of order".

Formal definition
Using the formulas above: n=1, v(x)=1, and d(x,y)=|x-y|. The directions on this spectrum are normally referred to as left and right.

Horseshoe theory
What is often called horseshoe theory claims that the extreme authoritarian economic left (Communism) is adjacent or close to extreme authoritarian economic right (neo-reactionism/fascism). A classification that follows this thought must then place these two close by or next to each other: either by using dimensions where they naturally fit next to each other, or by making opinion space curved so that going in the direction of fascism leads to Communism.

Two-dimensional


There are many two-dimensional political spaces. The Nolan chart and Political Compass are two popular examples, which can be seen as rotated versions of each other. The Pournelle chart is another variation with a different set of axes.

Three Telos Model
The Three Telos Model or Triangle Political Map is two-dimensional political model where voters tend to spread out in three directions. It describes political beliefs based on the core axiom of the philosophy, where the voter's depart from the center based on their core beliefs.

Each of the three colors (the "equality leftist", the "freedom liberal" and the "tradition conservative") have different criteria. The criteria are listed as:


 * Justification
 * Philosophical foundation
 * Prestige idenifier
 * Moral foundation (see Moral foundations theory on Wikipedia)
 * Vision of nature



Higher dimensions
Political opinion can be divided into essentially any number of dimensions. Some other examples include the 3-dimensional Sapply Compass, the 4-dimensional 8values space, and the 9Axes space.

One study of German voters found that at least four dimensions were required to adequately represent all political parties.

There has been references to many other political compasses that are similar, orthogonal or even contradictive.


 * https://www.reddit.com/r/Politicaltests/wiki/listoftests (archive https://archive.md/amTxo)
 * https://l-lists.com/en/lists/0isll4.html (archive https://archive.md/YATlp)
 * https://www.reddit.com/r/PoliticalCompass/comments/flzinl/list_of_every_test_i_know_including_some_you/ (https://archive.md/MOS9q)

Nonlinear spaces
Not all ways of classifying a political ideology need map to a cube or use the standard p-norm distances.

Different political philosophers also argue that a good political ideology must also incorporate additional constraints. For instance, from the liberal economic position, Milton Friedman advocated for the necessity of putting one of two desired values ahead of the other by stating "A society that puts equality before freedom will get neither. A society that puts freedom before equality will get a high degree of both". From the economic collectivist position, anarchist Mikhail Bakunin argued that a good political ideology must have both significant amounts of freedom and equality, stating that "Freedom without socialism is privilege and injustice; socialism without freedom is slavery and brutality". These positions are not incompatible since both argue for the same result however the difference lies in what is controlled and what is expected to arise naturally.

Such additional constraints would impose further structure on a political classification chart; however, it may still be useful to represent political ideologies that violate the constraints. Even if they are in some way suboptimal or are inherently self-contradictory, people may still hold them.

Calculations
Statistics that can be computed from a political spectrum and a set of candidates include:
 * Centrist bias
 * Mean minimum political distance