In an instance of size n of the stable marriage problem, each of n men and n women ranks the members of the opposite sex in order of preference. A stable matching is a complete matching of men and women such that no man and woman who are not partners both prefer each other to their actual partners under the matching. It is well known [2] that at least one stable matching exists for every stable marriage instance. However, the classical Gale-Shapley algorithm produces a marriage that greatly favors the men at the expense of the women, or vice versa. The problem arises of finding a stable matching that is optimal under some more equitable or egalitarian criterion of optimality. This problem was posed by Knuth [6] and has remained unsolved for some time. Here, the objective of maximizing the average (or, equivalently, the total) “satisfaction” of all people is used. This objective is achieved when a person's satisfaction is measured by the position of his/her partner in his/her preference list. By exploiting the structure of the set of all stable matchings, and using graph-theoretic methods, an O ( n 4 ) algorithm for this problem is derived.

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This paper presents an overview of New Hampshire's efforts to implement a pilot accountability system designed to support deeper learning for students and powerful organization change for schools and districts. The accountability pilot, referred to as Performance Assessment of Competency Education or PACE, is grounded in a competencybased educational approach designed to ensure that students have meaningful opportunities to achieve critical knowledge and skills. These opportunities are judged by the outcomes students achieve and not by inputs such as seat time. Therefore, students must achieve these competencies before moving on to the next major learning targets and/or graduating from high school. High quality performance assessments play a crucial role in the PACE system because of the need to have assessments that measure the depths of student understanding of these complex learning targets. Performance assessments are used as both summative and interim

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