Mate selection may be aimed at compensating specific shortcomings. For example, a mare may have superb gaits, but her legs are not of superior quality. The stallion of choice would need to have perfect legs, preferably with evidence that his offspring also have good legs. His legs would be considered more important that a strong trot, as the mare should bring that into the offspring. Another mare may have perfect legs but could have a somewhat stronger gallop, then the stallion should have an excellent gallop but is allowed to have somewhat lesser leg quality. At least, that is the idea. Specific mate choice for each female so that the offspring is of the best possible quality. A practical advice for breeding organisations would be to first select the parents as that defines the genetic improvement, and then define a compensation mating scheme as potential advisory service.
However, even though this sounds very logical, there is no guarantee for success! It is clear that with compensatory mating breeders will have different breeding goals that they base their mate choice on. Aspects of lesser quality in one female may be the stronger point in another female. Obviously, the additive effects of all mate decisions in a population is not likely to point in a certain direction. In other words, mating decisions will result in extra genetic gain. Also at individual level there are a number of factors that may influence the expected result of mate choice:
Mendelian sampling. This introduces a chance factor, even if you know the EBV for father and mother very accurately.
Pleiotropic (one gene affects multiple traits) and epistatic effects (gene-gene interactions). It is possible that a trait, for example gait quality in horses, is affected by a gene that interacts with another gene. If one of those genes has the wrong allele in the offspring then the gaits won’t be improved.
What is the accuracy of the information that the selection decision is based on? For example, does genetic or training make a champion? You should especially ask yourself such questions in the absence of an accurate EBV.
Thus:
Compensatory mating involves finding the best mate for individual females to compensate her shortcomings.
Compensatory mating may have an effect on individual mating results, but has not effect at population level.