In certain species only the dominant male gets to mate (or given strong preference), and yet the sex ratio remains 1:1. (I'm thinking in particular of gorillas). How does this happen? It doesn't seem like Fisher's argument should apply in this case.
Fisher's principle applies to such cases as much as it does to species where only pairs mate. Consider a species where a successful male has exclusive mating with a harem of 20 females, and for each such male, 19 other males are not able to mate. A female has 100% chance of mating, and a male has a 5% (1 in 20) chance of mating. Assume a female has two offspring.
In this scenario, an equal sex ratio would mean having a female offspring would lead to an expected number of grand-offspring of 2 (100% chance of 2 offspring from that female). Having a male offspring would also lead to an expected number of 2 grand-offspring (95% times 0 offspring plus 5% times 20 harem females each having 2 offspring).
What would happen if the ratio of births was off from 1 to 1, say 5 females were born for each male? Then expected number of grand offspring would be for a female is still 2, but for a male it is 25% (chance of taking a harem of 20 females against the 3 other males born alongside those 20 females) x 40 (20 harem matings x 2 offspring) = 10. Hence with a lopsided sex ratio in this situation, having a male is much more valuable genetically than having a female. If a mutant arose which produced more male offspring in this imbalanced situation, it would have success until the population sex ratio became close to 1:1.
mgkrebbs has already covered the maths that leads to the preservation of ratio, so I'll not recap.
You might have noticed that the argument only remains true if you don't know whether the particular male you produce is likely to be the dominant male or not. If you could "know" in advance that your particular son was more likely to be dominant it would make sense to skew their sex ratio towards male and vice versa. It may interest you to know that this actually happens.
Males born to high ranking females are more likely to succeed than males born to low ranking females. This makes intuitive sense as they'll get better access to food and the same genetic traits that help a female become dominant may help the male become dominant too. What's fascinating is that this actually leads to top ranking females having a male-skewed sex ratio among their offspring, and low ranking females having a female-skewed sex ratio.
See Great expectations: dominance, breeding success and offspring sex ratios in red deer for the original paper. I do not know what the mechanism behind the sex selection is.