Professor Gary Becker has some interesting comments on the illegality of polygamy and the likely effects of its legalisation. In part, he writes:
The claim that polygyny is unfair to women is strange since polygyny increases the demand for women as spouses in the same way that polyandry would increase the demand for men. If men were to take multiple wives, that increases the overall competition for women compared to a situation where each man can have at most one wife. This argument against polygyny is like arguing that a way to increase the economic prospects of minorities is to place an upper bound on how many members of these groups a company can employ. Of course, actual laws that try to improve the economic circumstances of minorities often in effect take the opposite form by placing lower, not upper, bounds on their employment in different companies. That too is not sensible but I save that for another day.
The entire article makes a number of worthwhile points. For example, as more and more societies move towards the recognition of civil unions between homosexuals as contracts equivalent to marriage, the traditional arguments against polygamy seem to be weakening.