Why Did God Allow Polygamy?
Although Scripture doesn't tell us specifically why God allowed men to have multiple wives, we can make an "informed" speculation. Here are some things to consider:

First, throughout much of history, there have been more women than men. Statistics show that about 50.5% of the current global population is female. According to the U.S. Bureau of the Census, the resident population of the United States, projected to 10/24/07 at 20:32 GMT (EST+5) is 303,202,568. As of Nov. 1, 2006, there were 152 million females in the United States and only 148 million males. That's 4 million more women than men. If the same percentages existed in Old Testament times, women would have outnumbered men by the tens of thousands.

Second, warfare back then was especially brutal, with an extremely high rate of fatality. This would have produced an even greater ratio of women over men.

Third, because of the patriarchal structure of ancient societies, it was next to impossible for women to provide for themselves. Most women were uneducated. Women depended heavily on their fathers, brothers, and husbands to provide and protect. Single women often ended up as either prostitutes or slaves.

Fourth, such a significant imbalance in the ratio of women to men would have left many, many women in an undesirable situation. It seems that God allowed polygamy to protect and provide for the women who could not find a husband otherwise. A man would take multiple wives, and serve as the provider and protector of all of them. Living in a polygamist household was far better than the alternatives: prostitution, slavery, starvation, etc.

Fifth, polygamy also enabled a much faster expansion of the human race, fulfilling God’s command to “be fruitful and multiply, fill the earth” (Genesis 9:7). Men are capable of impregnating multiple women in the same time period…causing humanity to grow much faster than if each man was only able to produce one child each year.

Again, these are only “informed” speculations.