Petition as defined by Webster's dictionary in the year 1828:
>PETI'TION, verb transitive To make a request to; to ask from; to solicit; particularly, to make supplication to a superior for some favor or right; as, to petition the legislature; to petition a court of chancery.
It's basically just an ask
The first amendment guarantees your ability to ask the government for shit.
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>I asked once if you in US have referendums of some sort, but did not got an answer
A referendum in the United States is an election.
We have them every November.
Some states will have "referendums" on things like: "Should weed be legal? Vote Yes or No."
So yes, we do have referendums.