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...

I know I mentioned it. Maybe I was too wordy. True, with equal servo arm and control horn lengths the mechanical advantage is one and there is neither an increase nor a decrease in torque. But the reason why you don't want to use a 2" arm instead of a 1" arm in your example is because given the same amount of desired control surface deflection, the 2" arm will move about a smaller arc, thus using less of the servo's resolution and you'll be operating closer to its deadband region. Likewise, any slop in you linkage will be more noticable if your servo's full operating range is within a 20 deg arc as opposed to a 40 deg arc. And lastly, a 2" arm will experience much more bending loads than a 1" arm, possibly causing unwanted deflections and even failure so it would have to be appropriately beefed up. The only advantage to the 2" I can see is better linearity response because there is less rise and fall of the pushrod due to less arcing (but that can be taken care of with expo).

-Tim