We may be about to step through some undergrad poli-sci and IPE coursework and (as inevitably happens) a review of book 1 of Plato's Republic up-thread, if you're interested. Or the poster may just leave it at a downvote and not respond. :-/

I tried to take Socrates' side of Book 1's exchange re: the definition of justice once already with another probably-libertarian, but we got derailed by your parent poster. (the short version for the uninitiated: if you try for a simple, inflexible, & complete definition of justice, you've almost certainly opened yourself to obvious contradictions and/or consequences that everyone hates as soon as you start gaming it out—workable definitions of justice that survive serious scrutiny are hard to come by)