The average-size conjecture for Selmer groups of elliptic curves

Let $K$ be a global field, and let $n$ be a positive integer. Consider all elliptic curves $E/K$, ordered by height, and write $\operatorname{Sel}_n(E)$ for the $n$-Selmer group of $E$.

Average-size conjecture. The average size of the $n$-Selmer groups is

$$\sum_{d\mid n}d.$$

This conjecture predicts the distribution of Selmer groups that underlies many average-rank results for elliptic curves over global fields. The supplied text gives no resolution of the conjecture in this generality.