On the earth today most animals use a two sex mating system where male and female provide the same amount of genetics to the resulting offspring, despite the fact that in many cases the female provides a disproportionately high degree of resources in producing and raising the young than the 'free-loading' male.
However, this isn't always the case. Some ants, and other insects, depend on a haplodiploidy mating system where a mother may pass on 2/3 of her genetics to her (female) offspring. There are other unusual mating systems hybridogenesis where a female may always clone part of her own genetics.
In a way these systems seem to make more 'evolutionary sense'. If a mother is going to contribute the majority of effort into raising the offspring she would have incentive to ensure that the child has more of her genetics, and a male that provides only 1/3 of his genes to a female can still be a viable means of passing on his genetics so long as he gets to mate with more than one female at a time. While a mother would want some degree of genes from a male to gain the advantages of sexual reproduction (resistance to disease, higher degree of adaptability to unusual circumstances, ability to pass on advantageous mutations to the species as a whole etc), she could theoretically gain most of these benefits even if her child only inherited 1/3 or even 1/4 of their genes from her partner. Her children would suffer slightly in adaptability in this situation, but the ability to pass on significantly more of her genes per child could easily be enough of a boon to be worth trading away a bit of survivability/adaptability per child due to the lowered genetic variety.
Is there a reason this system would not work for other species, and in particular for sapient species? Can I justify the evolution of a sapient alien species, preferably somewhat mammal-like if possible, where the mother passed on the majority of her genetics to a child while keeping a smaller percentage of genes (I'd guess 1/3 or 1/4 would be the most likely combinations) from her mate? I'm looking for highly social species, but not euro-social; that is to say one matriarch does not produce most of the children, and all individuals are generally competing for mating rights with each other as seen in most mammal herding species.
Assuming this is possible how would the differences in genetic contribution affect the standard evolutionary roles of the species? For instance males would presumably be less likely to contribute in the care-giving of the young now that each young has less of it's own genetics. Would males be born less often in such a species, defying the traditional fisher principle? would males on such a gambit still compete for female matings, and thus evolve to (on average) be larger and stronger to engage in competition with other males?