# Political spectrum

Wikipedia has an article on:

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.[1]

## Spatial models

Many spatial models of voting put voters and candidates in a multi-dimensional space, where each dimension represents a single political issue,[2][3] sub-component of an issue,[4] or candidate attribute,[5] even including non-political properties of the candidates, such as perceived corruption, health, etc.[2] Voters are then modeled as having an ideal point in this space, with a preference distance between themselves and each candidate (usually Euclidean distance), i.e. a voter may be closer to a candidate on gun control, but disagree on abortion. Voters are then modeled as voting for the candidates whose attributes or policy proposals are nearest to their ideal point (or strategically voting to try to minimize their distance to the actual winner).[6] Other models that follow the idea of “closeness” are called proximity models.[7]:93, 96

Mathematically (and spatially), a line on a political spectrum can be 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.

## 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:

## References

1. Refer to the Electowiki Point of View (EPOV)
2. a b Davis, Otto A.; Hinich, Melvin J.; Ordeshook, Peter C. (1970-01-01). "An Expository Development of a Mathematical Model of the Electoral Process". The American Political Science Review. 64 (2): 426–448. doi:10.2307/1953842. JSTOR 1953842. Since our model is multi-dimensional, we can incorporate all criteria which we normally associate with a citizen's voting decision process — issues, style, partisan identification, and the like.
3. Stoetzer, Lukas F.; Zittlau, Steffen (2015-07-01). "Multidimensional Spatial Voting with Non-separable Preferences". Political Analysis. 23 (3): 415–428. doi:10.1093/pan/mpv013. ISSN 1047-1987. The spatial model of voting is the work horse for theories and empirical models in many fields of political science research, such as the equilibrium analysis in mass elections ... the estimation of legislators’ ideal points ... and the study of voting behavior. ... Its generalization to the multidimensional policy space, the Weighted Euclidean Distance (WED) model ... forms the stable theoretical foundation upon which nearly all present variations, extensions, and applications of multidimensional spatial voting rest.
4. If voter preferences have more than one peak along a dimension, it needs to be decomposed into multiple dimensions that each only have a single peak. "We can satisfy our assumption about the form of the loss function if we increase the dimensionality of the analysis — by decomposing one dimension into two or more"
5. Tideman, T; Plassmann, Florenz (June 2008). "The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior". Assume that voters care about the “attributes” of candidates. These attributes form a multi-dimensional “attribute space.” Cite journal requires `|journal=` (help)
6. Woon, Jonathan. "Introduction to spatial modeling" (PDF). University of Pittsburgh.
7. Rabinowitz, George; Macdonald, Stuart Elaine (March 1989). "A directional theory of issue voting". American Political Science Review. 83 (1): 93–121. doi:10.2307/1956436. JSTOR 1956436.