He 'campaigned for president/governor/mayor'. = He 'campaigned' for the presidency/governorship/mayoralty. [=he tried to be elected president/governor/mayor]
The group launched/mounted/led a 'campaign' to protect the area from commercial development.
The university is organizing a 'campaign' to attract a more diverse student population.
(..) Hello. - Sir, this is Tony Stark. Welcome back to the land of the living. - We believe you're about to be drawn into the Mandarin campaign, and we've got to get you somewhere safe as soon as possible. Mr. Stark, I'm about to eat honey roast ham surrounded by the agency's finest. (..)2013 Iron Man 3