The minimum-degree four conjecture for majority edge list colourings

Let $G$ be a graph with minimum degree at least $4$. A list assignment gives each edge a list of colours, and a majority edge colouring from these lists assigns to every edge a colour from its list such that, at every vertex, no colour is used on more than half of the incident edges.

Minimum-degree four conjecture. Every graph with minimum degree at least $4$ admits a majority edge colouring from lists of size $3$.

This conjecture strengthens the known result that every graph without pendant edges admits a majority edge colouring from lists of size $4$. The source does not state whether the conjecture has been resolved.