Finite-population average treatment effect and weak null

Consider the no-interference binary-treatment submodel of Finite randomized treatment-assignment models in which the allowed assignment set is $\{0,1{\}}^{\mathcal{I}}$ and unit $i$'s response under assignment vector $z$ is $Y_i(z)=Y_i(z_i)$ for fixed real potential responses $Y_i(0)$ and $Y_i(1)$. For the fixed units, define the finite-population average treatment effect by ${\tau }_F:=\frac{1}{N}{\sum }_{i\in \mathcal{I}}(Y_i(1)-Y_i(0))\mathrm{.}$ The weak zero-average-effect null is the hypothesis ${\tau }_F=0$; it constrains the average of the unit-level effects, not each effect separately. The Fisher sharp null in this submodel, defined in Fisher sharp null and predeclared test orderings, requires $Y_i(1)=Y_i(0)$ for every unit. No probability distribution on the fixed potential responses is part of either definition.