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.
(..) Act on this we must. The capture of General Grievous will end this war. Quickly and decisively we should proceed. The chancellor has requested... that I lead the campaign. WINDU: The council will make up its own mind who is to go, not the chancellor. A master is needed, with more experience. (..)2005 Star Wars: Episode III - Revenge of the Sith