Evolution of the haplo-diplontic life cycle
I just want to report the finding of one paper here. I don't know much about the rest of the literature and can't comment on it.

Otto et al. (2015) investigate this question in sexually reproducing organisms. As I understand it, they assume that the amount of time spent in on phase of the life cycle is proportional to the amount of selection happening in this phase. With a theoretical model Otto et al. (2015) showed that there is a sexual conflict over the length of the haploid phase. Mothers favour a longer haploid phase while fathers favour a shorter haploid phase. The outcome of the model depends upon who is in control of the length of this phase.

For mothers, producing a baby is often costly (see Bateman's principle). As such, the mother might want to ensure that its baby has high fitness. In the haploid phase, deleterious recessive alleles are no masked by their dominant counterpart and hence can be purged out of the population. A long haploid phase, therefore allows purging of deleterious alleles and make the diploid phase more resistant which is in the mothers interest.

Among fathers, the evolutionary pressures are different. Fathers evolve to mask mutations carried by their haploid gametes (e.g., by provisioning with diploid gene products), causing their sperm to be more competitive. As such, a father has interest that the haploid phase is short.