概率分布相似最大化的“就近—随机”入学机会公平优化——以北京市西城区为例

Maximum Spatial Equality of Educational Opportunity Based on the Proximity-Random System:A Case Study of Xicheng District, Beijing

入学公平是社会关注的热点议题,对社会公平有重要的意义。既有研究表明,富裕阶层与优质教育资源之间存在的空间循环累积是造成基础教育入学机会不平等的重要原因,距离在其中有关键性的影响,这种现象普遍存在于就近入学等入学分配制度中。随机分配被认为是打破这种空间不平等机制的重要方式,目前已有城市开始试行。虽然地理学早在1960年代已经开始研究学区优化,且教育学正在出现"空间转向",但引入随机机制的学区优化研究仍很少。文章沿用学区优化研究中的交通类比传统,引入蒙特卡洛交通流模拟研究进行问题类比,进而定义"就近-随机"入学的公平优化问题,即寻求各个学校到各个小区最优的学位分配方式,使入学机会趋于空间均等化。采用概率分布描述入学机会,将入学机会空间公平定义为概率分布相似程度最大化;借鉴区划问题中属性距离的计算方法,将概率分布相似程度最大化问题转换为多维空间内概率分布向量的距离最小化问题,进而构建包含最大距离约束和学校容量约束的概率分布相似最大化"就近-随机"空间分配优化模型。以北京市西城区为例进行模型应用,采用PSO算法进行求解。结果表明,文章构建的模型可以显著提升入学机会的空间公平。文章还进一步讨论概率分布相似建模思路在其它公平优化研究中的可能应用。

Equal educational opportunity is a hot topic of social concern, which is of significance to social justice. The existing literatures have shown that the geographical mechanism between wealthy families and better school is the main reason of the educational inequality, on which geographical access has a substantial impact, and this mechanism prevails in popular systems such as proximity-based system. Random allocation about admission to the school is considered to be an effective approach for breaking such inequality, it has been trialed or planned in some cities. With an apparently growing "spatial turn" in education, although the geographical study on school planning can be traced back to 1960 s, it has few studies about the optimization of school districts based on the random allocation. Applying the transport analogy and simulation of Monte Carlo traffic flow, this paper explores the optimal allocation of enrollment opportunity equality based on the proximity-random system and realizes the spatial equality of enrollment opportunity of students. On the basis of the probability distribution, it defines the spatial equality of opportunity as the maximum similarities between possibility distributions. According to the calculation method of attribution distance in geographical regionalization problem, this paper converts the problem into minimizing total distance in multi-dimensional space in order to solve maximum similarities. A new spatial allocation optimization model which, toward equal educational opportunity, is developed to maximize the similarities between the probability distributions across demand nodes is applied to a case study of primary school allocation in the Xicheng District of Beijing and resolved by PSO. It suggests that this model can improve spatial equality of educational opportunity significantly. This paper also discusses the possibility for the optimization of other equality objectives.