Too many males can cost, in biological terms, the female. Females 'going' from one male to another are more exposed to injury, sexually transmitted diseases and predators, not to mention the wasted energy. In the polyandrous species, the female mates with more males.
Polyandry is widespread in nature. In 1 % of the birds, polyandry is the rule: nandu, cassowaries, some shore birds (like phalaropes), lily-trotters or buttonquails. Many frogs and reptile females, too, are highly promiscuous, but so are social spiders and insects, like beetles attacking stored food. The honey bee is the whore of the insect world, exhausting many drones....
Unlike in the case of the polygynous species (like the peacock), where the male is the active sex, in this case is the opposite: the females are the active sex. Females occupy the battlefield and chase away their weaker female rivals. Subsequently, only the bigger and brighter females will be fecundated by the males gathered around them and their descendants are more vigorous than the ones mothered by their rivals.
These females can be very aggressive and can destroy the eggs incubated by a male, just to make him incubate her eggs and raise her descendants. Typical for a male, isn't it?
In other birds, polyandry is more peaceful. In Galapagos hawks, a family is made by one female and at least 2 males helping her to raise the chicks.
In the case of the tamarin monkeys and other South American monkeys, the female is the boss and the family always contains two faithful husbands. The males of the family don't "fight" each other, either. They have to cooperate to take care of the offspring, soon after these are born. As the female usually gives birth to twins, each male will take care of one offspring that usually doesn't weigh more than 40 g at birth.
The cooperation takes place from the very moment they start courting the female. They will mate with her in turns, without the slightest conflict or jealousy. This way, each one of the two can 'believe' it has fathered the offspring. Other mammals are also polygynous, like some marsupials (Antechinus of Australia).
Some species are only apparently polyandrous, due to 'paternity biasing', as the female, even if mating with more males, will use just the sperm from the 'preferred' male to fertilize her eggs, or will take care only of the offspring fathered by her chosen mate.
But if you thought that only animals can be polyandrous, you're wrong. The marriage of a woman with more than one husband is extremely rare, but it does exist. The most common type of human polyandry is the fraternal one in which two (or more) brothers marry the same wife.
Various Himalayan nations practiced this: in Tibet, Kashmir, Nepal, Buthan, Ladakh, Arunachal Pradesh (northeastern India) and Mosuo people. The extinct culture of the Marquesan Islands (Pacific) practiced polyandry, but the phenomenon was also encountered amongst Amerindians (in the Canadian Arctic), Ceylon, Mongolia, South India (by Toda people) and some Sub-Saharan African tribes. Guanches, the original inhabitants of the Canary Islands, practiced polyandry as well.
There are tribal societies considering that a child could and should possess more than one father. In many cases (like that of Tibet), polyandry was caused by a need to retain aristocratic titles or lands within the family or due to frequent absence of the husband for long periods from the household (so that usually only one husband was present). Poor farmers, too, could not afford to divide their small agricultural lands.
Some anthropologists see in human polyandry a method of birth control, as the woman will have only one pregnancy, no matter the number of partners, while in polygyny, a man impregnates several women, resulting more children.