"How broken does a justice system have to be before vigilantism is moral?"
Moral to whom? Moral to the individual vigilante, moral to the society with a broken justice system, or moral to outside observers?
Should the form the vigilantism takes also be considered? In one society the vigilante act may be totally illegal whereas in another society it may be totally fine and as a matter of course carried out by the government itself and even protected by the Constitution.
Here's a case where a mom went into vigilante mode and now faces prosecution for the crime of publicly identifying the child who murdered her daughter.
https://www.independent.ie/irish-news/mother-who-posted-photo-online-of-one-of-the-boys-who-murdered-ana-kriegel-thought-it-was-wrong-they-are-protected-when-ana-was-not-41017846.html"Fitzpatrick told gardaí she could not understood how two juveniles could do something like that.
She said she had heard about the judge's order and that people could be brought to court and fined.
She admitted to sharing the material on Facebook, saying she had screenshotted the photo from someone else's page and then shared it.
She said she took it down two or three minutes later because people were texting her.
When asked by gardaí why she had shared the photo, Fitzpatrick said she questioned why the boys were being “hidden” when their actions were not the actions of juveniles and that the girl did not get a say in anything.
Fitzpatrick said she thought it is “wrong they are protected when she [Ana Kriégel] was not protected”.
She said she was sorry for the boys' families, but was not sorry for them."
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So hers was an act of vigilantism over there across the pond but in America it's not a crime and is done as a matter of course by our own government, by news organizations, and is protected speech under the First Amendment if a citizen does it.
https://firstamendmentcoalition.org/2009/06/can-i-publish-the-name-of-a-minor-involved-in-a-crime/"Can I publish the name of a minor involved in a crime?
Q: We printed the name of a 17-year-old arrested for car jacking. Now the mother is complaining and said we should not have legally named her kid. Does she have a case?
A: In general, under the First Amendment the truthful publication of the identity of a juvenile who has been accused of a serious crime cannot be punished. See Smith v. Daily Mail Publishing Co., 443 U.S. 97, 103 (1979). (Note: this case deals only with criminal sanctions, but other United States Supreme Court cases have held that accurate reports cannot give rise to civil liability, either. See Bartnicki v. Vopper, 532 U.S. 514 (2001).)
In California, the Supreme Court has held that the publication of the names of minors involved in crimes is not an invasion of privacy. See Kapellas v. Kofman, 1 Cal. 3d 20, 36-39 (1969). (Note that this case dealt with minors who were the children of a political candidate; however, the reports of recent crimes are consistently held to be newsworthy, so this is probably a distinction that makes no difference in the outcome.)If a report is based on information from a public record source, the law is even more clear. The accurate report of that information is absolutely privileged, both by statute (Civ. Code section 47) and by the First Amendment (see Gates v. Discovery Communications, Inc, 34 Cal.4th 679 (2004))."
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I just rewatched "24" and one thing along these lines that struck me was the provision for the granting of total immunity for crimes including murder and raping children in return for cooperation, knowing full well that the people would continue to commit the same crimes for instance an assassin who would be released in a foreign country where she could keep plying her trade. That made me wonder if we would have the right as citizens to know what types of crimes our government has provided immunity against prosecution for and to whom they have been provided and then have the ability as citizens to decide for ourselves if we want the elected representatives responsible for those decisions to have our vote next time or not.