A third possible intermediate position combines formal equality of opportunity with the requirement that state action should treat all citizens equally and not confer arbitrary advantages on some along with arbitrary disadvantages on others. On this view, even the substantive aspect of equality of opportunity is a deontological requirement, a moral constraint on permissible action, not a specification of a goal that morally ought to be achieved. Call this position the deontological requirement interpretation of equality of opportunity. Unlike FEO, the deontological requirement does not hold that substantive equality of opportunity is violated if some parents provide better educational opportunities for their children than other parents. The deontological requirement does not specify that a society must establish a system of state-funded education. But if the state does operate schools or provides funds to defray the costs of some children's education, the state violates the deontological requirement if its schools or disbursements of funds to parents earmarked for children do not operate in an evenhanded manner but instead arbitrarily confer advantages on some over others. Operating schools for Roman Catholics only or paying for the school tuition only of children who attend Roman Catholic schools would be clear cases of violation of the deontological interpretation. A perhaps more controversial example would be the operation by the state of public schools funded by general tax revenues that are formally open to all resident children but are physically accessible only to children who can walk normally or set at a level such that some severely retarded or otherwise cognitively impaired children can gain no benefit from the instruction that is provided. According to the deontological requirement of equal treatment, these policies would be violations of equality of opportunity if and only if they arbitrarily advantage some children and disadvantage others.