The Finite Selection Model (FSM) was developed by Carl Morris in the 1970s for the design of the RAND Health Insurance Experiment (HIE) (Morris 1979, Newhouse et al. 1993), one of the largest and most comprehensive social science experiments conducted in the U.S. The idea behind the FSM is that each treatment group takes its turns selecting units in a fair and random order to optimize a common assignment criterion. At each of its turns, a treatment group selects the available unit that maximally improves the combined quality of its resulting group of units in terms of the criterion. In the HIE and beyond, we revisit, formalize, and extend the FSM as a general tool for experimental design. Leveraging the idea of D-optimality, we propose and analyze a new selection criterion in the FSM. The FSM using the D-optimal selection function has no tuning parameters, is affine invariant, and when appropriate, retrieves several classical designs such as randomized block and matched-pair designs. For multi-arm experiments, we propose algorithms to generate a fair and random selection order of treatments. We demonstrate FSM's performance in a case study based on the HIE and in ten randomized studies from the health and social sciences. On average, the FSM achieves 68% better covariate balance than complete randomization and 56% better covariate balance than rerandomization in a typical study. We recommend the FSM be considered in experimental design for its conceptual simplicity, efficiency, and robustness.

翻译：有限选择模型（FSM）由卡尔·莫里斯在20世纪70年代为RAND健康保险实验（HIE）（Morris 1979，Newhouse等1993）的设计而提出，该实验是美国规模最大、最全面的社会科学实验之一。FSM的核心思想是：每个处理组以公平且随机的顺序依次选择单位，以优化共同的分配准则。在每一轮选择中，处理组选取当前可用的单位，该单位能使该组已选单位组合的总体质量在准则上获得最大提升。针对HIE及其后续应用，我们重新审视、形式化并扩展了FSM，将其作为实验设计的通用工具。借助D-最优性思想，我们提出并分析了FSM中的一种新选择准则。基于D-最优选择函数的FSM无调优参数、具有仿射不变性，并在适当情况下可还原出随机化区组设计、配对设计等经典实验设计。针对多臂实验，我们提出了生成公平且随机处理选择顺序的算法。我们通过基于HIE的案例研究以及健康与社会科学领域的十项随机化研究，展示了FSM的性能。平均而言，与完全随机化相比，FSM的协变量平衡性提升68%；与重随机化相比，平衡性提升56%。鉴于其概念简洁性、高效性和稳健性，我们建议在实验设计中考虑采用FSM。