Regarding causal inference in observational studies, in order to not violate the ignorability assumption (which states that outcomes are independent from treatment, given a set of covariates), one may make use of matching to obtain a stochastic balance, which is supposed to be seen in randomized controlled trials.
I have seen comments that in some circumstances, matching N samples in one group to 1 sample in the other group (let's say case and control), or vice-versa, could be a better strategy.
My question relates to what are such circumstances and how it should be done in these cases, for example.
Apparently, one of the uses of matching N:1 (Many-to-one) is to improve the results of matching by nearest-neighbor, a greedy algorithm that obtains a local optimum. One may repeat control samples, which increase your sample size, since you're matching k controls for every treated samples. The thing here is that with this, you have a bias-variance tradeoff. Less bias with pair matching (1:1) because the match is closer, but less efficient because you're discarding data (it can be a big problem if your sample size is already small). With many-to-one, you get a little more bias, but smaller variance. It's up for the person to decide if it's worthwhile to tolerate more bias for more efficiency.
However, I'm not sure if this is what the author (Jason Roy) meant, or what is meant in general, by circumstances where N:1 could be a better strategy.
This is a pretty good review of matching methodology and justification. I think it may help clear things up.
Article Matching Methods for Causal Inference: A Review and a Look Forward
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