Behavioural feasible set: Value alignment constraints on AI decision support

When organisations adopt commercial AI systems for decision support, they inherit value judgements embedded by vendors that are neither transparent nor renegotiable. The governance puzzle is not whether AI can support decisions but which recommendations the system can actually produce given how its vendor has configured it. I formalise this as a behavioural feasible set, the range of recommendations reachable under vendor-imposed alignment constraints, and characterise diagnostic thresholds for when organisational requirements exceed the system's flexibility. In scenario-based experiments using binary decision scenarios and multi-stakeholder ranking tasks, I show that alignment materially compresses this set. Comparing pre- and post-alignment variants of an open-weight model isolates the mechanism: alignment makes the system substantially less able to shift its recommendation even under legitimate contextual pressure. Leading commercial models exhibit comparable or greater rigidity. In multi-stakeholder tasks, alignment shifts implied stakeholder priorities rather than neutralising them, meaning organisations adopt embedded value orientations set upstream by the vendor. Organisations thus face a governance problem that better prompting cannot resolve: selecting a vendor partially determines which trade-offs remain negotiable and which stakeholder priorities are structurally embedded.