So a justice system is a public good. It contains people who are trying to sue. That counts as a personal vendetta, only arbitrated by the courts. Your juxtap

So a justice system is a public good. It contains people who are trying to sue. That counts as a personal vendetta, only arbitrated by the courts. Your juxtaposition of 'private interest' vs 'public interest' needs work. Evidently they can both be aligned.