Arnold Kling proposes that we use three separate sets of axes, one for Progressives, one for Conservatives, and one for libertarians. The advantage is that it is prescriptive about how each will process information, so you can (theoretically) better communicate with someone in another tribe.
For Progressives, the axis is Oppressed-Oppressor.
For Conservatives, the axis is Civilization-Barbarism.
For libertarians, the axis is freedom-coercion.
Kling explains the social revolution of the 1960s using this model:
Along the civilization-barbarism axis, they view it as a slide from civilization toward barbarism.This gives a suggestion on how to frame arguments. For example, a libertarian arguing against gun control with a Progressive might frame the discussion in terms of how past gun control laws were disproportionately targeted against oppressed minorities (c.f. Jim Crow laws) and that the expected impact of proposed legislation will disproportionately impact racial minorities and women.
Of course, progressives see it entirely differently. Along the oppressor-oppressed axis, they view the cultural changes as favorable, because women were liberated (a conservative would put scare quotes around “liberated”).
Along the libertarian’s coercion-freedom axis, the picture is mixed. On net, did the cultural changes lead to more or less government coercion? It is hard to say. For example, in the area of Civil Rights, I would argue that getting rid of Jim Crow laws reduced government coercion. (Note that in the early 1960s, prominent libertarians tended to take the states’ rights position, which strikes me as misguided.) However, there is a sense in which today government is overly intrusive on matters of race. (You may be happy with that if your concern is with the oppressor-oppressed axis, and you believe that government is helping the oppressed.) I would prefer that government model treating people as individuals by refusing to classify people by race (You may be very unhappy with my suggestion if you think that the oppressor-oppressed model is significant).
He also has a survey you can take to find out which of the three axes you primarily work on. Interesting stuff.
Of course, it may be that none of this matters because everything is about tribes.