Display (8), p. 16 — D^µ(≿_ab, ≿⁺_ab) = µ{b}

Let $X$ be a finite set, $\mu$ a positive measure on $2^X$, and $a,b\in X$ distinct. The relations $\succsim_{ab}$ (every alternative other than $a,b$ strictly above both $a$ and $b$, nothing else) and $\succsim^+_{ab}$ (the same, plus $a$ strictly above $b$) are acyclic orders, and

The value shows that $d(\succsim_{ab},\succsim^+_{ab})$ plays the role of the point mass $\mu\{b\}$ in Axiom 3, which is how the measure is recovered in the "only if" direction of Theorem 3.1.

Formalization Note $\mu\{b\}=w(b)$ for the point weights $w\ge0$. The two acyclicity conjuncts record that both relations lie in $\mathcal A(X)$, as the page's "partial orders" asserts.