FEO's requirement to equalize prospects functions as a social choice rule over competing educational regimes, making it structurally vulnerable to Arrow-type indeterminacy when regimes produce divergent relative rankings.

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Arrow-type indeterminacy(as used in decision theory and social choice theory): A logical problem (discovered by economist Kenneth Arrow) where it's impossible to rank multiple options fairly because different fair ranking methods give you different answers.
Divergent relative rankings(as used in comparing different educational approaches): When different educational systems rank students in opposite or conflicting ways—for example, System A says Student X is top-performing while System B says Student Y is top-performing.
Educational regimes(as used in education policy discussion): Different systems or approaches to organizing and running education—for example, different ways of structuring schools, curriculum, or student grouping.
Equalize prospects(as used in discussions of fairness): Making sure that people from different backgrounds have genuinely equal chances at success, not just equal access to the same resources.

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