This is taken from A Season with Verona by Tim Parks. It discusses solutions that have been tried, were successful, but shot down for reasons that may or may not be deduced easily.
"Was this, then, the game when it occurred to me that Italy should bring in foreign referees for Serie A games, men with other cultural backgrounds and mental constructs? I was proud of the idea and even thought of writing to some authority somewhere, until I discovered that the experiment had already been made in 1957. Presumably it was so successful that they had to stop it. Or perhaps the foreign referees simply adapted to the environment. Another corrective to the evident bias of refereeing was tried in 1984-85 when the refs for each game were selected entirely at random. That year Verona won the championship and again the experiment was terminated, or at least 'corrected'. Now the Federation draws up a short list of suitable refs for each game, then draws from that list by the lot. The football magazine entitled, wait for it, 'Rigore', is frequently able to 'predict' which name will come out of the urn."