Policymakers in the Department of Defense and Congress have expressed a normative goal that all levels of the armed forces ought to represent society, coupled with alarm over whether recruiting and promotion policy can keep up with society's rapidly changing demographics. This dissertation informs manpower policymakers seeking to achieve this goal of social representation by presenting three essays on obstacles to improving demographic representation in the armed forces. The first essay focuses on the effect of eligibility requirements on the demographic distribution of the population that is able to serve in the Air Force. The second essay focuses on Air Force Specialty Code (AFSC, i.e. occupation) assignment at the United States Air Force Academy (USAFA). Historically, Air Force personnel policies have demonstrated a preference for rated (i.e. flying) AFSCs by giving officers assigned to these AFSCs better promotion prospects. If these policies continue, the demographics of future senior leaders will tend to reflect the demographics of cadets who enter into these particular AFSCs. This essay summarizes demographic differences in AFSC assignments for the USAFA classes of 2004-2009 and models the assignments with probit regression and a two-sided logit methodology. The third essay performs a parallel analysis on the 2007 Army ROTC branch (occupation) assignments. Because Army ROTC assigns branches to cadets in a way similar to the Air Force Academy's AFSC classification process, this essay also employs the two-sided logit methodology.