Where would the cut off point be

Imagine a world where we have a new refereeing system.

In this system there is a panel of 100 qualified and unbiased referees who have an electronic machine with three buttons: "Left", "Right" and "No Touch". For every touch each referee will press a button. Each referee acts independently and is unable to see the decisions of other referees.

Let's say for a particular touch:

50 vote for "Left"

49 vote for "Right"

1 votes for "No Touch"

Do you think that Left should be awarded the touch?

How many votes should Left/Right need in order to be awarded the touch?

Would it ever be reasonable for no touch to be given, even if "No Touch" received a minority of votes?

For example:

35 vote for "Left"

34 vote for "Right"

31 vote for "No Touch"

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(I was thinking about this in the context of sabre but maybe a similar problem could be applied to foil?)

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