Two Kinds of Optimality

Allocation $x$ is ex ante Pareto-preferred to $y$ if for all $i$, $U^i(x^i)\geq U^i(y^i)$ with strict inequality for some $i$.

Allocation $x$ is ex ante Pareto-preferred to $y$ if for all $i$ and for all $s\geq 0$, $u_i(x^i_s)\geq u^i(y^i_s)$ with strict inequality for some $i$.

Theorem. If for all $i$ and $s\geq 1$, $\pi_i(s)>0$, then if $x$ is ex-ante Pareto-preferred to $y$, then $x$ is ex-post Pareto-preferred to $y$.

The converse to this theorem is false. Consider an exchange economy with two individuals, two states of the world and one consumption good. Draw the Edgeworth box and identify the ex ante and ex post optimal consumption allocations.