Eh? Humans make errors so the more humans the more errors? That logic makes no sense.
Assume ALL Refs on the pitch have to agree with a decision. If one Ref disagrees, the
Main Ref's decision is final, just as it is now.
1 Ref has the probability of success at 95% (figure made up for this example). He gets it right 95% of the time; 5% chance he is wrong.
2 identical Refs have a success rate of 95% each.
0.95^2 = 0.90 = 90% = There is 90% chance both Refs get the decision right. 10% chance one of them is wrong (and the decision falls back to the
Main Ref).
1 ref = 5% chance of getting it wrong
2 refs = 10% chance of one getting it wrong (and the decision falling back to the
Main Ref).
3 refs = 14% chance...
4 = 19%
5 = 23%
At no point does increasing the Refs increase the accuracy of the decision, only the chance of getting it wrong (and reverting back to the
Main Ref's decision).
So, adding more Refs does not help, it only hinders.
You could change the assumption. e.g. A vote by Refs on all decisions? Would only work with even numbers of Refs. I can't think of any more that don't lead back to the
Main Ref overriding all and thus being pointless.
(Been a long, long time since I did proper maths - someone correct me if I'm wrong. I don't mind being wrong. I wont take it personally.)