The veil of ignorance is a procedural mechanism that achieves impartiality without requiring substantive similarity, showing similarity is sufficient but not necessary for general will reasoning.

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Procedural mechanism(as used in philosophy of law and ethics): A step-by-step process or method designed to achieve a specific goal.
Substantive similarity(as used in epistemology and ethics): When two things are actually alike in their important features or characteristics (as opposed to just seeming similar on the surface).
Sufficient but not necessary(as used in logical conditions and arguments): Something that guarantees a result (sufficient) but isn't required for that result to happen another way (not necessary). Like: having a car is sufficient to get to work, but not necessary—you could take the bus instead.
general will(Rousseau's Social Contract): The collective will that emerges from an assembly of citizens, either through procedural constraints on self-interested deliberation or through the exercise of citizen virtue

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