Ranking multiple-input and multiple-output units is a critical problem that arises in a broad range of disciplines. While various methods have been proposed and applied, their comparative strengths and weaknesses are not well understood. In this paper, we assess and compare two popular methods, data envelopment analysis (DEA) and heuristic rank aggregation approach (i.e., the Borda method), in the context of ranking multiple-input and multiple-output units. Both methods exploit the output-input ratios, but in different ways. The Borda method sorts the units by taking the arithmetic average of the ranks in terms of individual output-input ratios, whereas DEA ranks the units based on composite output-input ratios. We use simulations to compare Borda rank aggregation and six DEA models, including CCR (Charnes, Cooper, Rhodes), super-efficiency CCR, BCC (Banker, Charnes, Cooper), super-efficiency BCC, SBM (slacks-based measure), and super-efficiency SBM. The simulations are based on Cobb-Douglas and translog production functions with both single output and multiple outputs. We show that the heuristic Borda rank aggregation, though simple to implement, performs better than DEA models for Cobb-Douglas production function under three situations: small sample size, relatively balanced weights for production factors, and presence of multiple outputs. For translog production function, the Borda method generally performs better than the CCR model, but cannot match up to other DEA models. We also demonstrate the performance of different methods via application to the well-known problem of ranking countries by human development. Our research sheds light on the potential of rank aggregation to complement or even supplant DEA under certain conditions.

对多输入和多输出单元进行排名是在广泛学科中出现的一个关键问题。尽管已经提出并应用了各种方法，但是它们的比较优势和劣势尚未得到很好的理解。在本文中，我们在对多输入和多输出单元进行排序的背景下，评估并比较了两种流行的方法，即数据包络分析（DEA）和启发式排序聚合方法（即Borda方法）。两种方法都利用输出-输入比率，但是方式不同。Borda方法通过根据各个输出-输入比率的等级算术平均值对单位进行排序，而DEA根据复合输出-输入比率对单位进行排名。我们使用模拟来比较Borda等级汇总和六个DEA模型，包括CCR（Charnes，Cooper，Rhodes），超高效CCR，BCC（银行家，Charnes，Cooper），超高效BCC，SBM（基于松弛的度量）和超高效SBM。这些模拟基于Cobb-Douglas和具有单输出和多输出的对数生产函数。我们表明，启发式Borda秩聚合虽然易于实现，但在以下三种情况下对Cobb-Douglas生产函数的表现优于DEA模型：样本量小，生产要素的权重相对平衡以及存在多个输出。对于跨日志生产功能，Borda方法通常比CCR模型表现更好，但无法与其他DEA模型匹配。我们还通过应用到人类发展排名国家这一众所周知的问题，论证了不同方法的性能。