tions of "how much" is enough. There might be an achievement level such that those who fall below it would be unlikely to be able to participate in the basic economic and political life of society. This suggests looking for a threshold level of some sort that defines how much input is needed to reach this level. Even if such a threshold level can be agreed upon, there will still be important questions to resolve. Threshold principles often apply to "all that are able," which involves not only judgments about the capacity of individuals but also about the resources society is willing to expend on teaching those with low capacity. Thus, there are choices to be made between setting the adequacy bar at a high level (and accepting that a larger number of students will not meet it) and a low level (which allows for fewer exceptions). On another front, deciding where to draw the line on quantitative adequacy must also take into account the possibility that there might be a law of diminishing returns, such that higher levels of educational resources result in ever-diminishing amounts of improvement in educational achievement or ultimate life chances.

Qualitative and quantitative adequacy thus raise numerous issues when considered independently; they also interact in ways that will pose additional challenges for the development of adequate school finance systems. For example, the interaction has interesting implications for the outcome of a state decision about whether or not to allow individual districts to provide more resources than called for by the state-determined "adequate" level. On one hand, let's say that a state school finance system embodies a broad definition of qualitative adequacy, incorporating most or all of the primary educational goods that will affect life chances significantly and/or that its quantitative adequacy level is sufficiently high that spending above the adequate level will not yield much in additional returns on the critical dimension of life chances. In this case, districts' freedom to spend whatever they want beyond the threshold may result in nice extras for students but will not compromise equality of opportunity. Such a "broad or high adequacy" policy is likely to be quite expensive and redistributive, however, and therefore politically unpopular with wealthier parents who would like to keep their resources in their local schools to benefit their own children. "Narrower or lower adequacy," on the other hand, erodes commitment to equality of opportunity by setting a floor under achievement that guarantees only participation in the basic institutions of society, not equal opportunity to enjoy all of society's primary goods.

Despite these difficulties, adequacy holds promise for overcoming two serious theoretical weaknesses with the more common concept of equality of opportunity. First, equality of opportunity—the idea that all children should have an equal chance to succeed and that education is one of the most efficient tools for ensuring this—is insufficiently attentive to which educational outcomes matter most in the sense of making an important contribution to the life prospects of individuals. Second, equal educational opportunity requires no particular level of achievement, nor does it forbid significant inequalities in achievement between

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