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A political spectrum is a system of classifying different political positions upon one or more geometric axes that symbolize independent political dimensions. - Political Spectrum - Wikipedia

The Nolan Chart is a political spectrum diagram. The chart divides human political views into two vectors—economic opinion and personal opinion—to produce a type of Cartesian chart. It expands political view analysis beyond the traditional "left–right" line, which measures politics along a one-dimensional line, into a graph with two dimensions: degrees of economic freedom and personal freedom. - Nolan Chart - Wikipedia

The Political compass (much more popular) is the Nolan chart rotated 45° clockwise and flipped vertically. Nolan's Chart + Political Compass

Is it true that radicals and reactionaries, falling on the edges of the compass, are the most deontological? And that centrists are the rational consequentialists? Is there a correlation? Or is it more complex and thus a 3rd axis would be informative?

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    The question would be benefit from a little introduction where you would mention that your purpose is to classify political opinion (or parties, or politicians) and precise what the two first axes are... – Evargalo Jun 4 '18 at 13:40
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    You will able to quantify its correlation to other measures with sample data. – Aaron Brick Jun 4 '18 at 15:48
  • I am closing this question as primarily opinion-based because which models are useful and which are not to quantify something as abstract as political opinion is completely subjective. Also note that the Nolan chart is far from the only system which attempts this. There are other "political compass" systems with different and more axis. I have seen some with 6 and more. – Philipp Jun 4 '18 at 18:46
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it seems to me that "radicals" and reactionaries (would fall on the edges of the chart/compass) are the most deontological. [i.e. rule or duty based]

and that centrists are the most (rational) consequentialists.

is the correlation more complicated than that and thus a 3rd axis would be useful?

No.

It would not be useful, because this presumes that people tend to have coherent deontological v. consequentialist ideologies.

In my experience, people do not have coherent ideologies in this regard and instead take different approaches on a case by case basis as it suits them without even realizing it.

In general, a deontological v. consequentialist ideology distinction, like distinctions between views about the political process, are almost always subordinate to other considerations which are reasonably well reflected by the existing two axes of the Political Compass.

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    Or as Goldwater said: extremism in the defense of liberty is no vice. Moderation in pursuit of justice is no virtue. – K Dog Jun 4 '18 at 17:39
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    I think people with a clear view you just be on the walls of the chart, while people with less clear opinions tending to solve the hypotheticals more or less evenly and end more in the middle. Just like few people stand for absolute personal liberty or personal suppression, but by how they answer cases they can be assigned a score on that axis. I do have trouble finding a use for noting the difference in a political context though. – user9389 Jun 4 '18 at 18:31

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