I'll bite my tongue and suggest mechanical advantage does not exist at less than a 1:1.1 ratio.

In any event I hope your example of 2" arm is nothing more than an example. The force at an arm length of 2" is only 77.5 ozs., coupled to a horn shorter than a 1:1 ratio would be garner undesirable results. The term mechanical dis-advantage comes to my mind.

All this said, never and I mean never set-up a control surface in such a method that you are operating with a mechanical disadvantage. The control horn should always be at least as big as the servo arm if not bigger so as to use mechanical advantage to your advantage....

Let me preface my statement regarding control horn over-all length being equal to or larger than the servo arm length. The over-all control horn length is measured from the surface's hinge pivot center-line to the pivot or attaching point of the push-rod at the control horn...