What do you call the opposite of a libertarian?

[🐒Gods of Prosperity🔱🐲💸]

The most logical term would be "authoritarian" since authority is more nearly an opposite of liberty than community is.   One may take a libertarian position for communitarian reasons, or have a communitarian account of what a more libertarian society could look like.  One may support an expansive, interventionist government for Hobbesian reasons, rather than any belief in a substantive, organic community. 

The problem is of course that "authoritarian" is a pejorative word, associated with awful regimes of past and present.  For example Pinochet, whose economic policies were influenced by libertarianism rather than following a "big government" program.   Still, if someone finds themselves unwilling to be designated "authoritarian," perhaps that shows they are not truly opposite to libertarian themselves, but rather see libertarian concerns as needing to be balanced?

In terms of a label for the upper left quadrant of a political matrix - I don't see an obvious answer.  The fact that this matrix originated with libertarians is clear here, as this quadrant represents less of a particular political tradition than the other quadrants, existing only as a compliment to the test's libertarian anchor.

But if I had to come up with a term  ... perhaps "protectivist" ?    That is, expressing an impulse to protect society and individuals from threats  - physical, economic, social, cultural - through active government.

[🐒Gods of Prosperity🔱🐲💸]

The most logical term would be "authoritarian" since authority is more nearly an opposite of liberty than community is.   One may take a libertarian position for communitarian reasons, or have a communitarian account of what a more libertarian society could look like.  One may support an expansive, interventionist government for Hobbesian reasons, rather than any belief in a substantive, organic community. 

I would disagree with this on the grounds that "authoritarian" is usually used to refer to a political system (i.e. "monarchy", "democracy", "dictatorship") rather than a set of political or social positions (abortion, taxes, environment). While the political economy of authoritarian regimes tends to gravitate towards state-led solutions, this is not a necessary component of such. I can see both "collectivist" and "statist" being more appropriate terms (albeit, perhaps more extreme than "communitarian").

Yes, I agree with you that "authoritarian" is not an appropriate term here due to the way it is normally used.  I just meant that the root words of "liberty" and "authority" provide a contrast, so one might think merely on that basis they would be opposites, in the absence of other definitions.