From The Economist’s Free Exchange:
Economists often argue that polygamy … benefits women because it enhances their market power. That’s because it means more marriageable men for every women. …
But once a woman enters into a polygamous arrangement, it seems she’d have less power. Bargaining power in a household is often based on who contributes what to household production and utility. Each person provides certain services and resources to make the household function and this keeps the marriage balanced. But the power structure is different when you have one man and several women. The marginal value each woman can uniquely provide diminishes the more women that are added to the family. …
You might argue that a woman retains some power because she can leave marriage and find someone else. After all, she has exceptional market power in the dating market. But terminating a marriage is costly, especially if the woman has children and is dependent on the man financially (and has no legal recognition). … Under these circumstances her market value declines as she ages.
I find the argument about declining power unconvincing. It appears to be an argument based on irrationality of the woman. These potential costs are not hidden and as for other marriages in liberal democracies, the woman can enter the marriage when and on the terms she sees fit. Yes, power may relatively decline, but that is part of the consideration of whether to marry. If there are any restrictions on her bargaining power, they are often in the form of state regulation of marriage and restrictions on pre-nuptial agreements. If polygamy was legal, a term of the marriage contract could concern other or potential wives.
There is another argument against polygamy that I find more convincing. In a polygamous society, there is an increase in the number of low-status men who will be unable to find a partner. Evolutionary theory would predict that those men are going to take whatever actions necessary to gain access to mates. In a June opinion piece, evolutionary biologist Rob Brooks wrote of the similar problem of excessive men due to sex selection:
In many animal species, when males overabound, they often compete so fiercely to court, win and even coerce the few available females into mating that everybody suffers. The same is true when the supply of men on the marriage market exceeds the demand from females.
In Bare Branches: The Security Implications of Asia’s Surplus Male Population, political scientists Valerie Hudson and Andrea den Boer argue that violent crime, gambling, drugs and the kidnapping and trafficking of women are rampant in places where there are too many men.
In his book Sex, Genes and Rock & Roll, Brooks addresses polygamy more directly:
The first possibility is that legal polygyny is incompatible with mature democracy. More than a century ago, George Bernard Shaw observed that ‘Any marriage system which condemns a majority of the population to celibacy will be violently wrecked on the pretext that it outrages morality’. He had the then-recent Mormon experience in mind when he observed that ‘Polygamy, when tried under modern democratic conditions…is wrecked by the revolt of the mass of inferior men who are condemned to celibacy by it’. Late in the twentieth century, biologists picked up on this idea. Richard Alexander argued that it becomes ever more difficult for wealthy polygynous leaders to retain the political support of lower-status men when those men cannot marry and reproduce.
Polygyny is, in the long term, incompatible with a smooth-functioning democracy because it promotes the deepest evolutionary interests of the wealthiest and most powerful men at the expense of all other men and all women. Despotic and bloody rule allowed kings and emperors of old to amass phenomenal wealth, marry prolifically and keep harems. But wherever circumstances have made it more difficult for despots to rule, the elites found it easier to gain the loyalty and support of their subjects if those subjects had the stake in society that marriage and family brings, and if the elites were themselves visibly monogamous. Most of the countries where polygyny remains legal are countries where democratic governance, if it is present at all, has only recently superseded dictatorship or monarchy. We can predict that in those countries where democracy matures, the state will cease to sanction polygyny.
In some ways, there is already some monopolisation of females by high-status men through serial marriages and mistresses. Many low-status men are unable to obtain a partner regardless of the legality of polygamy. However, policies that increase that tendency can lead to trouble. Mating is not a zero-sum game, and this is one area where, despite leaning towards the legalisation of polygamy (or more precisely, the exit of the state from regulation of marriage), I would be watching what occurs very closely.
If we ran that experiment, my gut instinct is that in developed nations, legalised polygamy would see limited occurrence of multiple wives (or husbands) and would hardly change the probability of most men finding partners. How many men do you know that could hold two wives?