In the season 1 trailer, observant players noticed a sixth chap walking about in the background of the summoner chamber. While there was speculation about observer mode, Noosh cleared it up on this forum:
Originally Posted by RiotBabagahnoosh
He's an arbiter/referee assigned to oversee the battle arena. There is one assigned to each team that fights in a Field of Justice. The actual battle arena takes care of itself via magic from the nexus that powers it.
In the learning center article about the League, we have the line; "The Adjudicators are the arbiters assigned to a given match in the Fields of Justice.
So. There you have it.
From this we can extrapolate a bit. If a group of summoners requires a referee, it is apparent that summoners are bound by a system of rules they have the capacity to break, or that situations can arise between teams that require an on-site judge. I would assume some thought has been given to the high emotional involvement that can accompany an important league fight despite how summoners Should be highly respectable individuals, and the possibility that a raging summoner of considerable power might need to be subdued..