Strongly equitable Ore-degree list-coloring conjecture

For a graph $G$, define its Ore-degree by

$$\Theta(G):=\max\{d(x)+d(y):xy\in E(G)\}.$$

A graph is SE $k$-choosable if every $k$-list assignment admits a strongly equitable list coloring. Strongly equitable Ore-degree conjecture. If

$$2k>\Theta(G),$$

then $G$ is SE $k$-choosable. This is proposed as the strongly equitable analogue of the Ore-degree list-coloring conjecture.