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Vector Politics

Vector Politics

Are you a "right winger"  or a "leftie"? Most people respond, "well, it depends on the issue".  In other words, "right" and "left" are wholly inadequate adjectives to describe a typical person's political viewpoint. Vector Politics attempts to deal with the inherent complexity of politics by adding additional dimensions to describe a person's viewpoints.  In the limit, as many dimensions may be added as necessary to describe distinctly different issues but care must be used to insure that the issues are "orthogonal" or unrelated. The vector distance between two viewpoints predicts how much overall disagreement exists between two individuals, and, similarly, the dot product of two vectors indicates the level of common interest. It will be proposed that individuals exist in a vector field, suggesting a scientific approach to predicting a person's changing political views over time.

Right and Left

In the United States people are categorized as either to the right or to the left, based upon their most powerful beliefs. People on the left might be there because of their belief in a strong centralized government, environmental protection, certain freedoms, non-typical lifestyles, a particular economic system or animosity for capitalism and its practitioners. On the right are found people who believe in minimal government, certain other freedoms, a free marketplace for ideas and commerce, and a concept of individual autonomy or liberty. As one can imagine, such sweeping generalities leave room for a lot of overlap and seeming contradictions. Political debate is reduced to pointing out the "hypocrisy" of holding one one-phrase described view while supporting a seemingly contradictory one-phrase described position. For example, how can one support the "right to life" and also support the death penalty? For those that hold those views, it is a stupid question and really seems more like a word trick. Political views can't be captured by single words or short phrases for most people.

Two Dimensions

A simple modification to "left" and "right" is to add a vertical dimension, "up" and "down". Lets say that those who are "up" tend to believe in a higher authority, typically either God or government, whereas those who are "down" typically believe in individual liberty and autonomy. Suddenly there is a two-dimensional space upon which individuals may be placed (fig. 1).  A conservative religious leader would most likely be upper-right and a big-government socialist might be upper left and be found to have similar types of views if not the same views on certain topics.  A Libertarian would be straight down and those liberals and conservatives that have strong Libertarian leanings might be right next to each other on each side of the vertical axis, agreeing more often than they like! In fig. 1, I attempted to place a few well-known individuals for illustrative purposes only. You might disagree on their proper placement.

Figure 1: Two-Dimensional Political Viewpoint Chart

The straight-line distance between two individuals in this two-dimensional space is proportional to how much they tend to disagree. An upper-left communist doesn't have much in common with a lower-right conservative Libertarian. In this improved but still simple topology, much is still lumped into the "left" and "right" horizontal axis and additional dimensions are needed to satisfactorily describe a complex person's political positions but the addition of this second dimension is a significant improvement over a single dimension and serves to illustrate the principle. It may also be the case that there is a topography to this two-dimensional map that might predict the most likely direction for people holding certain views to drift over time. If it is true that Liberals tend to become more conservative over time one might expect a counter-clockwise tendency. A Socialist or Communist might tend to become more fond of individual liberty, dropping down on the graph and similarly, the lower-left individual might tend to move to the right. If the topology continues, the lower-left Libertarian conservative might begin to "find religion" as he gets older or even to begin to believe in more government, moving vertically on the chart. Whether there is a wall between the left and right at the top of the chart is open to speculation. Do religious conservatives become more socialistic as time passes? How about conservatives that believe in government power in certain areas of life, say, social security for example? Or, perhaps the natural rotation is clockwise. Or the wanderings may be person-dependent and take just about any path. The counter-clockwise arrow of fig. 1 is only intended to illustrate the concept. The author fancies a counter-clockwise whirlpool where, if you live long enough, you end up at the center of the chart and reach for the channel changer when the political news comes on, saying, " eh, there ain't a lick 'o difference between 'em".  The "force" that a person feels depends upon his position on the chart and this distribution of forces is called a "field" just like an electric or gravitational field.


The obvious extension of the two-dimensional approach is more dimensions. To the extent that political issues can be defined such that they are independent from each other (what mathematicians would call "orthogonal") they can be assigned their own vector direction. Once the number gets above three, the resulting political space becomes too complex to imagine or graph and Vector Algebra techniques become more useful. A vector is a string of numbers that represents values for a set of independent variables. In this case, the values would be the strength and sign of a person's political position on certain issues.  Descriptive names could be given to the members of the set of dimensions like "up-down" for the higher authority vector as described above, "high-low" for drug legalization, etc. Obviously, it is impossible to assign precise numeric values to a person's viewpoints and assigning integer values to quantization phrases like "agree, strongly agree, disagree, etc. " gives all the precision that is practical. For simplicity, we assume that a negative opinion results in a negative numeric value. Another complexity is that it will not be a simple matter to couch issues such that they are orthogonal. Thus the values in the vector may not be truly independent. Despite these inaccuracies, the politician that positions himself at the tip of the public's aggregate multi-dimensional vector will be quite popular and an ace panderer!

Vector/Matrix Algebra

bulletIn N-dimensional space, the amount of disagreement between two parties may be determined by calculating the vector distance between their positions. The method is simple; determine the numeric distance between the individuals on each orthogonal issue, square them, add the squared values for all issues, and take the square-root. The answer is the absolute distance, politically speaking, between the parties in a high-order political space.
bulletThe "dot product" of two vectors determines their  commonality and indicates the overlap of interests between two subjects and the sign of the dot product gives some indication of whether they would be comfortable with each other's positions. Two individuals with a very small dot product might have little to agree or disagree about since they share few common political interests.
bulletIt is interesting to speculate what a cross product might yield; a candidate that holds positions described by the cross product vector of two different individuals would have managed to proclaim positions that don't concern either of them!
bulletVector addition, subtraction and averaging might be useful in determining the ultimate positions held by committees and other groups.
bulletA vector field is an intriguing idea where an N-dimensional field would describe the "force" on an individual's views much like the above topography analogy. Whether partial derivatives could be calculated is questionable given the difficulty of assigning anything approaching accurate values.  Perhaps a "lumpy" geometry, something akin to taxicab geometry or Boolean geometry is indicated for handling the discrete nature of political views  (or at least the difficulty in quantizing those views).


A more sophisticated mechanism for labeling political viewpoints has been proposed. It is suggested that vector algebra techniques might help politicians analyze the political landscape and help to clarify the differences between groups seemingly on the same side. Perhaps labels  beyond "left" and "right" might be adopted to quickly communicate a person's basic positions, the simplest being an additional "up" or "down" adjective. More complex labels might come about; "I'm a right-winger" doesn't carry the information that "I'm an upper-right-low-down-fast-outer" carries.  :  )