It sounds broad, but if you narrow it down, I think it could be very interesting. My recommendation would be to split it up into multiple questions.
What you want is to formulate "meritocracy" explicitly so that questions about it can be studied mathematically. If you already have a way of doing this, that's awesome. If not, your first question should be something along the lines of "How can I formulate 'meritocracy' mathematically?" which would include some properties you think must be satisfied by your definition of meritocracy, as well as a general description of the questions you're interested in answering about it. Questions to develop a definition may be "soft", but they are still acceptable (desirable, even) when asked with focus and proper context.
After you have a good mathematical definition for meritocracy, you want to come up with some explicit mathematical questions to ask about it, and ask these separately. You already have one:
- Can two participants in a meritocracy have identical initial conditions?
Note that once you have your definition, this question may wind up being somewhat meaningless, and develop into something more like
- What is the difference in expected outcome between those of equal natural ability but different initial conditions?
To address these, you'll need to decide how to incorporate the notions of initial conditions, actions, natural ability, and outcomes into your definition. Are actions probabilistic? Are outcomes real numbers (e.g. total wealth over a lifetime)? Are initial conditions (or natural ability) inherited from parents? How are outcomes determined? These would be good things to consider when constructing your meritocracy definition, but try to keep it simple at first, to prevent overwhelm.
Some other examples of questions you might want to consider using your definition:
What is the long term behavior of meritocracy? Is it stable?
Does meritocracy necessarily lead to a generational accumulation of power?
How much can a participant in a meritocracy be affected by random chance events in life?
Again, if you already have a few of these questions in mind, it would be relevant to include them as context in your initial formulation question, since these may affect what goes into the formulation, e.g. to study generational affects of meritocracy, your mathematical formulation of meritocracy ought to be compatible with generations. (But make sure you state explicitly that they are there for context, not to be answered, so you don't get closed for being too broad.)