Other forms: recall elections
When people vote to remove an official from office before the end of their term, it's a recall election. If enough voters think the new mayor is doing a terrible job, the city may hold a recall election.
A recall election is the opposite of a regular election; instead of choosing their favorite candidate, voters weigh in on whether an existing official should be forced to step down. Some recall elections have to be initiated by a higher authority, but many can be started by citizens who demonstrate enough support for the idea by collecting signatures. Recall in this political sense stems from the Latin revocare, "rescind, revoke, or call back."