We assume all systems are products of natural selection, so all strategies provide optimal survival of young. We ought to be able to predict mating system if we know enough about environment.
If you are not monogamous, you must not need full attention of both parents. If you have 1 male + 3 females, then this must be better than 1 m + 1 f. Obviously (?) this increases the chance of success for the male (even at some loss of success in any given nest) so long as he can pull it off. But it is the female who does the choosing, since she makes the metabolic investment in gametes. So a 3 female territory must be an optimal situation for producing young out of each nest.
WHY polygamy? Studies of Red-winged Blackbirds show that males arrive first and set up territories. [Draw 2 boxes, male A with female; male B without.] WHY WOULD AN INCOMING FEMALE CHOOSE MALE-A? A's territory must be really much better than B's.
Within breeding populations, most polygnyous birds are marsh edge birds. Productivity is greatest at water's edge and female reproductive success depends on territory richness. Polygamy also occurs in hole nesters that use abandoned holes. Black-capped Chickadees' nesting holes are a limited resource and are nonrandomly distributed. A female has no choice if male's territory has 2 holes in it. (Chickadees are one of the few passerines that mate for life--of 200 Song Sparrows banded, only 8 remained with same mate the following spring.) Eastern Bluebirds are similar but studies show polygamous birds may have reduced reproductive success from females' fighting (males taken out experimentally).
Is polygamy a consequence of skewed sex ratios? or differential survival (what with males' being brighter)? This has not been documented.