The rank-cover conjecture for CNA+ measures

Let $\mu$ be a CNA+ measure, and condition it on the total rank $\sum_eX_e$. Rank-cover conjecture. For each $k$, the conditional distribution given total rank $k+1$ stochastically dominates the conditional distribution given total rank $k$. The paper presents this as a conjectural extension of a lemma proved for a more restricted class of measures.