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.

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.

Calculations

Statistics that can be computed from a political spectrum and a set of candidates include:

• Centrist bias
• Mean minimum political distance