Rational quotient conjecture for special fibrations

Let $f:X\dashrightarrow Y$ be a special fibration with $\kappa(Y,f)=-\infty$. Let $\Delta(f)$ be its base orbifold, and let $\kappa$-rationally generated mean that the general orbifold fibre has the corresponding $\kappa$-rational generation property. Rational quotient conjecture. There should exist a unique fibration

$$r_f:(Y/\Delta(f))\dashrightarrow R(f)$$

such that the general orbifold fibre of $r_f$ is $\kappa$-rationally generated and

$$\kappa(R(f)/\Delta(r_f,\Delta(f)))=\kappa(R(f),r_f\circ f)\geq 0.$$

The source calls $r_f$ the rational quotient of $f$ and presents its existence and uniqueness as conjectural.