Wait, there's more than one side? Oh right... politicians and voters. The rich and dishonest vs. the saps. I don't care whether the guy or gal getting the reach around from lobbyists has a donkey or an elephant on their lapel... they're all jackasses to me.
And for what it's worth it's socialized (not socialist) medicine.
Defined by Merriam-Webster as "medical and hospital services for the members of a class or population administered by an organized group (as a state agency) and paid for from funds obtained usually by assessments, philanthropy, or taxation"
There's no definition for the term "socialized justice" because there isn't a great deal of debate as to whether government does a better job (not a good job, just a better job) of meting out justice than an impromptu cadre of individuals. The debate about the quality of tax payer health care vs. private ("free market" health care) is quite lively. I think suggesting there is any contradiction in accepting crime and punishment as a government institution while refusing health care as a government institution is based on a spurious sort of logic.