How to compare the efficiency of two encoding schemes or hypothesis languages?
The answer was just tree depth. What I needed to do was learn about evaluating the complexity of finite automata and how we can use a decision-tree model (decision-tree complexity) to put bounds on the complexity of an automata (analysis of algorithms). So I take my two coding schemes (call them A and B) and I make binary decision tree to predict the output of my system based on the inputs provided by the coding schemes. If both coding schemes A and B are equally useful for predicting the outputs but A requires a tree depth of 15 while B requires a tree depth of 54 then A is "better".  This is because our decision-tree model of the system is simpler when using A than when using B and as stated before we strongly believe that our system is as simple as possible. 

Of course I also need to include the complexity of the coding scheme itself but that just goes with alphabet size since it is a Nearest Neighbor search. 

So it was under my nose, I just needed some context.