How should one evaluate the ethics of polygyny (men having more than one wife) from the perspective of an Aristotelian, a Kantian, and a utilitarian ethos?
Kantian. There are two reasons that a Kantian might regard polygyny as immoral. First, if we restrict our attention on men as moral agents, it is largely and in most cases inconsistent to will that "Marry multiple women," be a universal maxim, because there aren't enough women for all men to marry more than one. Strictly speaking, this is not universally true. If population growth rates are fast enough and men marry much younger women, universal polygyny could be possible. Also, in the wake of large wars male populations are sometimes sufficiently depleted that the remaining men could practice generalized polygyny. Still, where populations are stable and/or spouses are roughly the same age, and where there have been no demography-altering calamities, if some men have two wives, others will have to go without.
Second, if we extend our attention to women as moral agents, a universal maxim to "Marry multiple people," making marriage exclusive on neither side, would clearly destroy the character of marriage altogether. However, to apply the same sexual morality to men and women is not unproblematic. Men have a biological reason to desire exclusive devotion from their mates that does not apply to women, namely that unless their mates are faithful, men will not know the paternity of any children they bear. More generally, women may have different sexual needs and desires than men do, such that ethical maxims appropriate for men could not be validly cross-applied. "Don't initiate romances; let the initiative come from the other side" might be a tenable, perhaps even wise maxim for women, but would hardly produce good results if practiced by both sexes, while "In situations of danger to yourself and your mate, value the other's safety above your own to the extent of sacrificing your life if necessary," might be a correct maxim for men, but would create oddities if applied to both sexes alike. I think the false application of universalizability to sex is one reason why the case for free love can seem so overwhelming to logical young males: since promiscuous sex appeals to the untrained masculine nature, "do unto others as you would have them do unto you," combined with an assumption of gender equality, seems to be a formula for free love. But this overemphasizes the body at the expense of the mind. If marriage is to be a connection of minds as well as of bodies, it does make sense to demand that maxims about marriage be universalizable to women as well as men, and to condemn polygyny on the grounds that polygynous husbands don't want their wives to practice polyandry, too.
Utilitarian. Presumably, as a rule, a man gets more (marginal) pleasure from his first wife than his second, and less still from his third. If so, to distribute women equally among men, in pairs of one husband, one wife, would yield more happiness to men than polygynous arrangements in which some men get several wives, others none. Polygyny can fuel social conflict, as some men are left frustrated and with "nothing to lose." Also, although the torments of jealousy suffered by women in polygynous arrangements may (at least "selfish gene" logic gives reason to think so) be less than those suffered by lovers of unfaithful women, the tug-of-war of wives for the attentions of one husband are surely painful. The Chinese film Raise the Red Lantern poignantly portrays the rivalries among the wives of a polygynous Chinese gentleman. So there are, it seems, pretty strong reasons to presume that monogamy serves the "greatest good of the greatest number." A survey of the world's monogamous and polygynous societies suggests that the former are more peaceful, dynamic and creative, as well as a possible reason: when men can have multiple wives, men's efforts may be devoted to competing for a scarce resource, what is called a "zero-sum game," whereas if they are strictly limited to one, sexual competition is greatly reduced, and competitive energies are directed more into positive-sum games like commerce, art, and scholarship.
Aristotelian. I don't know, but I expect Aristotle disapproved of polygyny, which was not practiced in Greece, as this article observes:
To a modern western audience, the fact that ancient Greeks and Romans were not supposed to be married to more than one person at any given time, nor even to cohabit with others alongside legal spouses, must seem perfectly ‘normal’. This may explain why this practice has received hardly any attention from historians of the classical world. Yet from a global, cross-cultural perspective, there is nothing ‘normal’ or unremarkable about this. Instead, until very recently, polygynous arrangements of marriage or cohabitation were the norm in world history, and strict monogamy remained an exception. Barely one in six of the 1,195 societies surveyed in the largest anthropological dataset have been classified as ‘monogamous’, while polygyny was frequently considered the preferred choice even if it failed to be common in practice (Gray (1998) 89-90, with Clark (1998)). Smaller samples of better documented societies convey a similar picture, and while ‘monogamy’ is observed in a small proportion of all cases (16-20% in samples of 348 and 862 systems: Murdock (1967); Burton et al. (1996)), due to their failure to distinguish between rare instances of polygamy and its formal prohibition these surveys tend to overestimate the actual incidence of strictly monogamous rules. In fact, although the nature of the evidence does not allow us to rule out the existence of strictly monogamous systems prior to the first millennium BCE, the earliest unequivocal documentation originates from the archaic Greek and early Roman periods. Thus, even though Greeks and Romans need not have been the first cultures to prescribe monogamy, these are the earliest securely attested cases and, moreover, established a paradigm for subsequent periods that eventually attained global dominance. In this sense, Greco-Roman monogamy may well be the single most important phenomenon of ancient history that has remained widely unrecognized. What is more, the global positive correlation between patricentric kinship systems and polygyny (Burton et al. (1996) 93-4) renders the emergence of prescriptive monogamy in the patricentric societies of Greece and Rome even more remarkable.
However, I doubt whether an Aristotelian meta-ethics really lends itself to the rejection of polygyny. Aristotle's measure of ethics was the realization of a man's telos, which was conceived as parallel to the "flourishing" of biological organisms. Clearly, for a male of any species to "flourish" in the biological sense involves polygyny. The reasoning of Darwin, or Dawkins, makes this especially clear, but the fact that polygyny for the wealthy and successful of human societies has been the general practice is evidence enough. Thus King David and the prophet Muhammad were polygynous, as is Osama bin Laden; the Bible treats King David's polygyny unproblematically as evidence of his success and glory. Even today, the polygynous impulse is not dead among the successful. US presidents can't be polygamous by law but many of them-- Warren G. Harding, Franklin D. Roosevelt, John F. Kennedy, Lyndon Johnson, Bill Clinton-- have been in practice. If we see a picture of a Hollywood star with a beautiful woman on each arm, it's a symbol of success. I once saw a crude wrestling type sport in which the contestants each came with a girl, and the victor in each match appropriated his opponent's girl, so that the winner ended up with four of them clustered around him.
I'm sure Aristotelian ethicists can find ways to argue that polygyny is not ("really") the height of human flourishing, and I'd probably agree, in a way, with the arguments they would make. And yet it seems clear to me that the real reasons polygyny is wrong are the Kantian and utilitarian ones, namely, that to practice polygyny is inegalitarian and causes unhappiness in others. Of course, I would also agree that man does not flourish, in the most important sense, by being polygynous: his soul does not flourish. But that is because the flourishing of a man's soul depends on his doing what is right, and Kant and the utilitarians can tell us why polygyny is not right, and therefore, why it is harmful to the soul. "Natural man," so to speak, flourishes by being polygynous; but man is not only a natural, but also a supernatural being. Supernatural man flourishes better when monogamous or celibate; polygyny is a burden to him; but this is only an illustration of the more general point that the flourishing of supernatural man has hardly anything to do with the flourishing of natural man and is often opposed to it. Man's soul may attain its utmost health just as his body is being ripped aparts by lions in the arena.