Sorry for the possibly stupid question, but how do petitions work? I'm from Russia, we have such things, but no one ever pays attention to them. For me, it's just a button on the Internet, not a "Voice that defends the rights of the people and/or individuals." (I'm sorry for the mistakes, you know, I don't speak English perfectly :p)
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In the case of what Arc linked, it's not a regular petition, but rather a request to the ACLU, American Civil Liberties Union, to push the petition forward as a request through, and should it not be followed, will use any means necessary, including and especially legal actions in the courts, to force a decision and mandate, to attempt to resolve the matter.
It's not a petition in the sense that it's a bunch of signatures saying "we want ___", but rather an effort from an activist and legal group to attempt to bring about change.