Randomization in social and clinical experiments is generally accepted as the “gold standard” for causal conclusions, because it balances baseline covariates across treatment groups on average, yielding unbiased causal effects. However, although randomization balances baseline covariates on average, it is possible that covariates could still be imbalanced just by random chance, compromising the validity of results. Although chance imbalance is often thought of as a rare, unlucky occurrence, it actually is quite common. For example, with only 10 independent covariates, there is a 40 percent chance that at least one will be significantly (using α = 0.05) different at baseline, just by random chance! Why subject your RCT to this kind of risk? If baseline covariates are thought to matter, balance should be checked at the time of randomization, before the experiment is conducted, and allocations yielding unacceptable balance should be eliminated.
Rerandomization (Morgan and Rubin, 2012) provides a way to avoid this chance imbalance for baseline covariates available at the time of randomization. Rerandomization works by checking balance at the time of randomization and rerandomizing if balance is unacceptable according to pre-specified criteria for acceptable balance. This process continues until an allocation with acceptable balance is achieved, and only then is treatment actually administered. When the criteria for acceptable balance is objective and specified in advance, and when treatment groups are equally sized, rerandomization maintains overall unbiasedness while also guarding against conditional bias due to chance imbalance. Thus we preserve the “gold standard” benefits of randomization, while avoiding detrimental chance imbalances; an idea Tukey (1993) called the “platinum standard.”From https://healthpolicy.usc.edu/evidence-base/rerandomization-what-is-it-and-why-should-you-use-it-for-random-assignment/
The problem with re-randomization is the same as the problem with matching: you measure and increase the balance on observables, which could decrease the balance on unobserved variables that are ~ uncorrelated with the observed variables. (See here for a simple simulation.) If everyone does re-randomization to increase the balance on the same observed variables, the nice aspect of experimental inference—unbiasedness in expectation—may not hold. Caveat emptor!