There is an interesting discussion on at the Becker-Posner Blog about the legality of Polygamy. Now I think it is a cool idea, but as Bono might say, Posner thinks in mysterious ways.
My view is that polygamy would impose substantial social costs in a modern Western-type society that probably would not be offset by the benefits to the parties to polygamous marriages. Especially given the large disparities in wealth in the United States, legalizing polygamy would enable wealthy men to have multiple wives, even harems, which would reduce the supply of women to men of lower incomes and thus aggravate inequality. The resulting shortage of women would lead to queuing, and thus to a high age of marriage for men, which in turn would increase the demand for prostitution. Moreover, intense competition for women would lower the age of marriage for women, which would be likely to result in less investment by them in education (because household production is a substitute for market production) and therefore reduce women's market output.No no that is not all, here is some more
In polygamous households, the father invests less time in the upbringing of his children, because there are more of them. There is also less reciprocal affection between husband and wife, because they spend less time together. Household goverance under polygamy is bound to be more hierarchical than in monogamous marriage, because the household is larger and the ties of affection weaker; as a result, "agency costs" are higher and so the principal (the husband, as head of the household) has to devise and implement means of supervision that would be unnecessary in a monogamous household. (An additional factor is that women in a polygamous household have a greater incentive to commit adultery since they have less frequent sex with, and affection for, their husband, so the husband has to watch them more carefully to prevent their straying.) This managerial responsibility deflects the husband from more socially productive activities.. But one man, brings out the real basis of the fear against polygamy
It potentially destabilizes a society in which the total number of men and women are roughly equal. So, for every man with four wives, there are three other sexually frustrated men with nobody.There it is.
So in a democracy, the number of frustrated people would always be more, hence a law against polygamy will always win. Hence, if you want more wives, get out of the bloody democracy.