You don't have to have an umpire or controller to run a campaign, but most players would agree that things go better if a person is nominated as overall umpire. The umpire can interpret the rules and improvise new ones, keep the players informed about forthcoming battles and invent special events, spread rumours and generally keep the campaign going. An umpire can be one of the players, or he can be someone who devotes all of his time to running the campaign and does not play himself. Another option is for different players to take it in turns to be umpire, sharing the burden equally.
The most useful thing that an umpire can do is publish a regular campaign newsletter in which battles fought over the previous weeks are summarised, the defeated are mocked, players are listed and their achievements recorded. Victorious players can place notices of their success and ridicule their enemies. The newsletter can also be used to announce local events and special games.
The opportunity to play God is probably as much fun as actually fighting the battles, and an imaginative umpire can make a big contribution to a campaign. He can also ensure that players don't deliberately avoid fighting enemies whom they fear will beat them, and can impose penalties on players that fail to show up for games. The umpire can also draw the campaign to a close once the players start to lose interest or one player gains ascendancy. All campaigns, even the very best, come to an end at some point, and it's generally better to make sure this happens sooner rather than later. Leave your players eager for more so that they join up for the next campaign with alacrity!
Finally, bear in mind that a campaign is not wholly fair or perfectly balanced. They aren't, and aren't meant to be. Part of the challenge of a campaign is to fight a battle against the odds - after all, if you lose such a battle it doesn't mean much, while if you win, the glory is greatly enhanced! In any case, a good umpire will be able to even things out without displaying blatant favouritism.