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The Finite Selection Model (FSM) was developed by Carl Morris in the 1970sfor the design of the RAND Health Insurance Experiment (HIE) (Morris 1979,Newhouse et al. 1993), one of the largest and most comprehensive social scienceexperiments conducted in the U.S. The idea behind the FSM is that eachtreatment group takes its turns selecting units in a fair and random order tooptimize a common assignment criterion. At each of its turns, a treatment groupselects the available unit that maximally improves the combined quality of itsresulting group of units in terms of the criterion. In the HIE and beyond, werevisit, formalize, and extend the FSM as a general tool for experimentaldesign.  Leveraging the idea of D-optimality, we propose and analyze a new selectioncriterion in the FSM. The FSM using the D-optimal selection function has notuning parameters, is affine invariant, and when appropriate, retrieves severalclassical designs such as randomized block and matched-pair designs. Formulti-arm experiments, we propose algorithms to generate a fair and randomselection order of treatments. We demonstrate FSM's performance in a case studybased on the HIE and in ten randomized studies from the health and socialsciences. On average, the FSM achieves 68% better covariate balance thancomplete randomization and 56% better covariate balance than rerandomization ina typical study. We recommend the FSM be considered in experimental design forits conceptual simplicity, efficiency, and robustness.

Balanced and Robust Randomized Treatment Assignments: The Finite Selection Model for the Health Insurance Experiment and Beyond