Becker has posed an intriguing question: if a woman thinks she would be better off as a second or third (or nth) wife rather than as a first and only wife, or not married at all, why should government intervene and prohibit the arrangement? From an economic standpoint, a contract that makes no one worse off increases social welfare, since it must make both of the contracting parties better off; otherwise they would not both agree to the contract.
The question has achieved a certain topicality because of the movement to legalize homosexual marriage. One of the standard objections to such marriage is that if homosexual marriage is permitted, why not polygamous marriage? The basic argument for homosexual marriage is that it promotes the welfare of homosexual couples without hurting anybody else. That seems to be equally the case for polygamous marriage.
But is it? 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. (For elaboration, see my book Sex and Reason (1992), particularly Chapter 9.) 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.
Of course, forbidding the wealthy to buy a particular commodity is usually inferior to taxation as a method of reducing inequality. Yet we do forbid the buying of votes, which could be thought a parallel device to forbidding the "buying" of wives: one vote, one wife. We think that vote buying would have undesirable political consequences. So might polygamy. In societies in which polygamy is permitted without any limitation on the number of wives, wealthy households become clans, since all the children of a polygamous household are related through having the same father, no matter how many different mothers they have. These clans can become so powerful as to threaten the state's monopoly of political power; this is one of the historical reasons for the abolition of polygamy, though it would be unlikely to pose a serious danger to the stability of American government.
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.
A woman who wanted a monogamous marriage could presumably negotiate a marital contract that would forbid the husband to take additional wives without her consent. However, she would have to buy this concession from the husband, which would make her worse off than if he were denied the right (in the absence of a contractual waiver of it) to take additional wives. Allowing polygamy would thus alter the distribution of wealth among women as well as among men.
Against all this it can be argued that polygamy would be uncommon in a society such as that of twenty-first century United States. But the less common it is, the fewer the benefits to be anticipated from legalizing it. And I am not sure that it would be all that uncommon. Although few American couples want to have more than two or three children, a polygamous union is not a couple. If a couple has three children, the ratio of adults to children is 2:3. In a polygamous household consisting of a husband, two wives, and four children, the ratio of adults to children is higher: 3:4. So the per-parent burden is less, even though there are more children.
Because polygamy is illegal everywhere in the United States, few Americans think of it as an option. If it were made respectable by being legalized, who knows? There are 400 American billionaires, and several million Americans with a net worth of at least $6 million. Nor, with most women working, is it obvious that a man would have to be wealthy in order to attract multiple wives, though presumably men who wanted to be polygamists would have to be able to offer some financial inducements, since most women would prefer to be a man's only wife. As more and more men attempted to become polygamists, the "price" they would have to pay for a wife would rise, so polygamy would be a distinctly minority institution. But it would not necessarily be trivial in size or harmless in its social consequences, which would be likely to exceed those of homosexual marriage. Polygamy is banned in most advanced societies and flourishes chiefly in backward ones, particularly in Africa. This is some evidence against legalizing it.