For homosexual animals, how would a female win over another female instead of fighting for her like a male?

Ok, before you feel the need of telling me that animals are not homosexuals (or that they are), or that asking specifically about females is just...a bit narrowed minded, let me explain that this is a question written in Quora and I have copied it here just in the way it was written.
Here is the complete question:

For homosexual animals, how would a female win over another female instead of fighting for her like a male?
Like a deer, a female usually doesn't have antlers, so she can't fight heterosexual males. How would homosexuality play for females in order to impress a mate? Again, a bird, a male bird has flashy colors while a female has camouflage, so homosexual female birds?

Well, the author of the question is apparently appaled by what they think it is a lack of chances for "homosexual" females, that lack in their opinion strength and appeal to attract or fight for another female...
hmmm...
If it were this way homosexual behavior in females would be very weird. But not, there are a bunch of examples that tell us that this is not the case.
Another answer on Quora (so long and thnks for all the fish, yes). Enjoy...
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 If the animals "follow" the rules of the species, it is not neccessary to "fight". For example, female deers in the same harem don't have to fight any male to have an homosexual moment.
So, the interesting thing here is to find some species in which females want to form their own homosexual unions fighting males. And in spite that -in gneral- scientists are quite more focused in what males do, yes, there are some studied cases of stable female unions that exclude temporaly males. And what seems to be the norm in these cases is that females choose to form the bond, they don't have to fight males to attract females, although this doesn't exclude that both females have to fight males that want to break their bond.

- Japanesse macaques is one example.  In some populations (notice the word population), homosexual behaviour among females is not only common, it's the norm. 
The pairings can even last a whole week, mounting hundreds of times.  When they're not mating, the females stay close together to sleep and  groom, and defend each other from possible rivals. Males don't just have to compete with other males for access to females: they have to compete with females too. In this species there is sexual dimorphism (Males weigh on average 11.3 kg , while females average 8.4 kg. Macaques from colder areas tend to weigh more than ones from warmer areas).
So what seems to explain the atachment between the females is pure and simple sexual attraction and the deed of them. So, females don't have to fight to gain females, they just choose each other, at least for some weeks.
But, these females don't exclude posterior mating with males.

Another interesting case, is the Laysan albatros which nests in Hawaii.
Among  them, pairs are usually "married" for life. It takes two  parents working together to rear a chick successfully.
But in one population on the island of Oahu, 31% of the pairings are made up of two unrelated females.  What's more, they rear chicks, fathered by males that are already in a  committed pair but which sneak matings with one or both of the females.  Like male-female pairs, these female-female pairs can only rear one  chick in a season. Again, in this case, it is the choice of the females, that don't exclude mating with males, what we see.

Source: http://www.bbc.com/earth/story/2...