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 → ℜ
• a distance function d: V × V → ℜ 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

The simplest example of a political spectrum is the uniform linear political spectrum, in which n=1, v(x)=1, and d(x,y)=|x-y|. The directions on this spectrum are normally referred to as left and right.

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.

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)

Three Telos Model

The Three Telos Model or Triangle Political Map is a way to describe political beliefs based on the core axiom of the philosophy. It is based on the concept of a ternary plot where the different underlying philosophies can be mixed but must sum up to the totality of the of the persons ideological position.

A video explanation of this model is provided by "ShortFatOtaku" on YouTube.

	Equity/Equality of outcome	Freedom/Liberty	Tradition
Justification	It is fair and reduces harm	People have a need for self-determination	People have attachments to the practices that tie them to a community, and changing society rapidly can be destructive.
Philosophical Foundation	Young Hegelians, Critical theory and Marxism	Liberalism and Enlightenment Humanism	Ancient philosophy and Right Hegelians
Prestige Identifier	Victim Culture	Dignity culture	Honour Culture
Economics	Marxism/Socialism	Free Market Capitalism	Mercantilism / Feudalism
Structure	Flat	Meritocratic / competence hierarchy	Inherited Cast / Class Hierarchy
Power holder	Government	Worthy	Cast / Class
Basic unit	Group / Collective	individual	Family / Tribe
Truth source	Postmodern denial of truth	scientific method	Divine Knowledge
World view	Power Structures	Materialism	Idealism
Moral Foundation	Care	Liberty	Loyalty/Authority/Sanctity
Vision of Nature	Unconstrained Utopian	Constrained Emergent	Constrained Structured

Ideology Placement

As in the two dimensional maps like the political compass, the differing ideologies can be put onto this map.

Nonlinear spaces

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

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.

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