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keywords:
auctions and market based systems
gtep
Student placements under diversity constraints are a common practice globally. This paper addresses the selection of students by a single school under a \emph{one-to-one convention}, where students can belong to multiple types but are counted only once based on one type. While existing algorithms in both economics and computer science have been designed to help schools meet diversity goals and priorities, we show that these methods can lead to significant imbalances among students with different type combinations.
To resolve this issue, we introduce a new property called \emph{balanced representation}, which aims to ensure fair representation across all types and type combinations. We propose a novel choice function that uniquely satisfies four critical properties: maximal diversity, non-wastefulness, balanced representation, and justified envy-freeness. While previous work has focused on developing efficient algorithms based on ranked reservation graphs, we propose an alternative approach using flow networks. This approach allows us to formalize the problem more compactly and achieve significant improvements in computational efficiency. We then propose efficient algorithms for implementing the choice function within both the ranked reservation graph framework and the flow network framework.