Polygamy can be seen from a social standpoint and also from a spiritual standpoint.
Explanation from spiritual standpoint:From SB 5.5.18, we understand that a man should not accept a wife (even one wife) if he cannot deliver his wife from the cycle of birth and death. The only way to deliver a soul from samsara is if the husband and wife both put Krishna in the center and serve Krishna. This is the goal of Grahastha Ashram otherwise a marriage solely for each other's pleasure (husband and wife's pleasure) is called grihamedhi (please refer to SB 3.32.1 for definition of grihamedhi). Unfortunately, marriage in the 21st century is solely done to enjoy as husband and wife. Such marriages are against Vedic injunctions.
Explanation from social standpoint:"According to our Vedic process, polygamy is allowed. For example, Krishna married sixteen thousand wives, Arjuna married three or four wives, Krishna's father, Vasudeva, married sixteen or eighteen wives, like that. So according to the Vedic system, polygamy is not prohibited, but it is not a farce also. Every wife must be provided for sufficiently. Krishna married sixteen thousand wives, but each wife was provided a palace, and He was personally present at each palace. It does not mean to marry many wives and maintain none of them. If anyone is able to keep more than one wife and give them all comforts of life there is no objection for having more than one wife. But if he creates trouble by marrying, he should not marry even one wife." - Srila Prabhupada - from the Book The Great Transcendental Adventure by Kurma Dasa
The basic point is, from a social standpoint, women are to be protected and if in a community there are more women than men, then one man can marry more than one women simply to prevent women from being abused and misused by unscrupulous men. However, if the man who is marrying cannot properly satisfy the women in all aspects (including mentally and emotionally), then the man is prohibited from marrying more than one wife. In the above quote, Srila Prabhupada is saying that a man should not even marry if he is a troublemaker for even one wife what to speak of more than one.
Therefore, to sum up;
- The goal of marriage is to put Krishna in the center and deliver one from the cycle of birth and death. Anything not this, is not marriage or a farce as Prabhupada mentions.
- Men can marry more than one women ONLY if the man can satisfy all wives equally without causing trouble even to one wife. In the above quote, Srila Prabhupada gives example of how great Kings and the Supreme Lord Himself accepted because they were highly competent to satisfy all wives equally. Ordinary human beings of this day and age cannot even satisfy one wife, what to speak of many.