I don't get this constant talk about registering to vote from the Americans. Do they need to register for every election?

Yes. Mostly because people are constantly trying to remove voters from the registry. And if you're not registered, you don't get a ballot. iirc, they also have different ballots if you're voting republican or democrat (in some places at least) ... which is why you need to register.

It depends on the jurisdiction, since elections are run by state/local boards. In NY, you only have to reregister if you move. However, I have to reapply for an absentee ballot every 5 yrs. Other states have different rules. vote.gov/register/

Register to vote in U.S. elections | Vote.gov

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