Many job markets can be characterized as two-sided matching markets, where hiring outcomes result from the intersection of two "quality sorts" between applicants and hiring organizations. While economists have detailed how these markets clear with respect to individual preferences, sociologists have tended to focus on the non-market features that stratify organizations or bias employment. This paper uses a simulation model of academic job markets to bridge these two literatures by asking (a) whether stable quality rankings emerge naturally within such markets, (b) how variation in agreement on applicant/organizational quality shapes market outcomes, and (c) whether (and under what conditions) an organizational caste system (Burris ASR 2004) might emerge. While this project is in the early working stages, preliminary results suggest that net of simple supply and demand features that shape market size, the extent to which organizations agree on applicant quality is a primary determinant of market outcomes. Resulting quality rankings tend to be very stable under most conditions, but employment exchange structures consistent with an organizational caste system emerge most frequently when there is a strong correlation between student and department quality