Which of the following is the most basic compound?
I agree with Doctor Insult's argument that "the stronger the base, weaker is the conjugate acid." In that sense, higher the $\mathrm{p}K_\mathrm{a}$ of acid, weaker is the acid, and hence, stronger is the conjugate base. The $\mathrm{p}K_\mathrm{a1}$ values of $\ce{HBr}$, $\ce{H2S}$, $\ce{H3P}$, and $\ce{H4Si}$ are -8.7, 6.89, 27, and ~35, respectively (Ref.1). Therefore, the order of the strength of their conjugate bases should be:
$$\ce{H3Si- \gt H2P- \gt HS- \gt Br-}$$
Hence, strongest base is $\ce{H3Si-}$.

Note: Ironically, this is the same decreasing order of electronegativity of center atoms $\ce{Si, P, S, Br}$: $1.90 \lt 2.19 \lt 2.58 \lt 2.96$, respectively.

References:


William L. Jolly, In Modern Inorganic Chemistry; 1st Edn.; McGraw-Hill, Inc.: New York, NY, 1984, p 177.