Starcraft is an example of a game that came closer to being "balanced" while still being quite "original" or "interesting".

They used a few tricks to make it possible for them to balance the game easier - such as: They accepted as necessary the rule that all races have the exact same resource need / ability to harvest ... thereby defining a base value unit ... the "crystal".

But they added a wrinkle that makes balance slightly harder to verify ... because they have a "gas" resource with different aquisition rules / limits than crystal and much different aquisition rules when viewed in terms of time (gas is missing at first, plentifull in early mid game, short and slow for later game technology, and all that is left in the final moments of a game that has gone on too long). [Ignore this tangent for the rest of my post - we will act as if gas does not exist in the game, since all races are affected by it in a very similar manner].

Once the value unit is defined, they seem to have decide to evaluate piece in 2 ways ... the first is sheer hit-points / damage capability. This is simple and straitforward to do ... but it doesn't tell the whole story, because another aspect enters into it - the number or percentage of situations in which the unit would be suitable to hurt the enemy, the number of tactical moves the unit has (movement type, speed, size, burrowing, etc) ... these are all things which do not affect a units value when in a pitched battle, but affect the players ability to set up favorable tactical situations (a very sun-tzu like concept). An example is the Protoss scout vs the Zerg Mutalisk I believe in the fairly early game mutas delivered more killing capability per unit money and time ... but they have a MUCH smaller health, and therefore are not "savable" units to the extent that scouts are. And latter in the game the scouts get increased speed, which makes them the most mobile / savable unit in the game.

The aspects of game theory / balance which these issues are based on are fairly easy to explore and discuss, but I really can't see a reasonable complexity that would allow an objective evaluation. I expect that 50 years from now a game like starcraft will be completely analyzable in the manner you suggest, but I believe given today's primitive understanding and theory of such things, it is simply beyond our current means to do anything but play test.

Basically I feel that your thesis can only hope to discuss terminology and some selective heuristics to apply to the balancing effort, and perhaps a few primative (but usefull) algorithms or at least processes that can be iterated to cover certainlow hanging subsets ... but I wish you great luck.