Political ideology is observed via a political spectrum with three axis: economic freedom (more = conservative, or less = liberal), foreign affairs (isolationism = conservative, or internationalism = liberal), and style of government (elite government, favoring Executive Branch = conservative or populace-oriented government, favoring Administrative Branch = liberal). Politicians, ideals, varying groups, and, most importantly, political parties can be placed on the spectrum based on their stances on those three topics.
To look at each current political party, you compare their stances on each of these three issues. Each political party can be placed and you can see which parties they are most in agreement to and least in agreement to (keep in mind this is a general outline, many parties differ in other more specific views than in these three issues):
|Political Party||Economics||Government||Foreign Affairs|
Thus, by the information compiled here, it's easily observable that the Progressive Party is completely opposite in views to the Establishment Party. Similarly, the Union and Socialist parties are completely opposite in views of each other, as are the Libertarian Party and Cosmopolitan Party.
Major Executive Maine and his Chief of Staff Theodore Crown were the first to quantify the exact political orientation, direction, and extremity of each party. Though the work was unfinished before Maine left office, Crown finalized the work and was able to plot each political party (using historical evidence, votes of members, and their platforms) in an X (economic), Y (government), Z (foreign affairs) coordinate so as to measure distance from each other and begin working to find an algorithm to help new members find the party they are closest in mindset to so that it would easier for them to join.
Maine and Crown did use the additional weighting of issues which several politicians and political scientists within the Triumvirate, most notably Andrew Mearl (the second Speaker of the Administration) and Carlson Tyler (the third Speaker), had advocated for: 1.5 weight on economic issues, 1.0 on government, and 0.75 on foreign affairs. What this mean was that, in general and for example, people felt twice as strongly on economic issues than they did on foreign affairs. Using (1.5, 1, 0.75) as the maximum coordinate (signifying perfect liberalism on every issue) and (0, 0, 0) as the minimum coordinate (signifying perfect conservatism on every issue, they discovered this plotting of each party as such (along with the distances between parties):
|Party||Progressive (1.2, 0.88, 0.69)||Authority (1.44, 1.0, 0)||Cosmopolitan (1.17, 0.12, 0.69)||Union (0.5, 0.24, 0.69)||Libertarian (0.04, 0.76, 0.06)||Establishment (0.11, 0, 0.06)|
|Authority||0.74 (closest)||1.15||1.39 (farthest)||1.42||1.67 (farthest)|
|Cosmopolitan||0.76||1.15||0.68 (closest)||1.44 (farthest)||1.24|
|Libertarian||1.33||1.42||1.44 (farthest)||0.94||0.76 (closest)|
|Establishment||1.37 (farthest)||1.67 (farthest)||1.24||0.78||0.76 (closest)|
From this, you can generally observe which parties are able to work together on various issues and which parties tend to ally based on liberal-conservative ideals. The most polar opposites, interestingly enough, are the Establishment Party and Authority Party, with an extreme 1.67 distance in views. The two closest in views are the Union Party and Cosmopolitan Party, with a slim 0.68 distance in views.