You still have a difference between solidary vs. selfish on the one hand and authoritarian vs. libertarian on the other. Authoritarian enforcement of solidarity is not unheard of (just look at the "forced collectivizations" in the Republican rearguard during Spain's civil war, as well as the gradual Stalinist takeover of the Republican side). It is probably the case that there is a correlation between the two axes but there is enough variation in the other direction to make two axes necessary, both with selfish libertarians (Randian/Hayekian neoliberals, anarchocapitalists...) and "authoritarian solidarity" (assorted left movements from violent "liberation" movements to the Pol Pots, Stalins and Maos of this world).

En un viejo país ineficiente, algo así como España entre dos guerras civiles, poseer una casa y poca hacienda y memoria ninguna. -- Gil de Biedma