Let L ϕ ( μ ) {L^\phi }(\mu ) be an Orlicz space and X ⊆ L ϕ ( μ ) X \subseteq {L^\phi }(\mu ) an ideal such that I ϕ ( f / | | f | | ) = 1 {I_\phi }(f/||f||) = 1 for each f ∈ X ∖ { 0 } f \in X\backslash \left \{ 0 \right \} . Then the unit ball B X {B_X} is stable, that is, the midpoint map Φ 1 / 2 : B X × B X → B X {\Phi _{1/2}}:{B_X} \times {B_X} \to {B_X} defined by Φ 1 / 2 ( x , y ) = 1 2 ( x + y ) {\Phi _{1/2}}(x,y) = \tfrac {1}{2}(x + y) , is open. In particular, B E ϕ {B_E}\phi is stable, E ϕ {E^\phi } being the subspace of finite elements of L ϕ ( μ ) {L^\phi }(\mu ) (i.e., f ∈ E ϕ f \in {E^\phi } iff I ϕ ( λ f ) > + ∞ {I_\phi }(\lambda f) > + \infty for each λ > 0 \lambda > 0 ), and B L ϕ ( μ ) {B_{{L^\phi }(\mu )}} is stable when ϕ \phi satisfies condition ( Δ 2 ) ({\Delta _2}) or ( δ 2 ) ({\delta _2}) , depending on the measure μ \mu .