What about a lord with no knights, or a lord with 5 knights? If this score is made to mean anything, and the scale is exponential, it'll just incite the realm to micro-manage knights to dump as many of them in as few regions as possible. On the other hand, if it's not exponential, then it'd be nothing more than a noble count meter.
P.S. I think it's cumulative, not exponential.
