Suppose each person were allowed to marry many. One argument is that this would be extremely complex because each man would have multiple spouses and each of those spouses would in turn have multiple spouses. But how is this a problem? Maybe there will need to be more paperwork. It's not a serious problem. Take employment as an example. One person may have three part-time jobs and the third person who hires him may work for another person and also hire several other people. This creates a bit of a mess when income tax forms need to be filled in but otherwise it's no hassle. That's what accountants and lawyers are for!
Another argument against this idea is that since there is a fairly equal distribution of men and women there would be a lot of people left out. But would this really be the case? Suppose you have five men and five women in a fictitious 10-person society. Suppose one man-the alpha male-is extremely rich and power he managed to take all the women. The four other guys miss out. However, this assumes that the women don't get a choice. Each woman can choose to marry four of the other men for instance. However, this could be a problem if the alpha male forbids the females he marries from marrying with other males. The alpha male is able to do this maybe because he is rich and powerful and the females don't want to lose him so the other four men lose out. However, if we had normal monogomy then those five females will all want the alpha male and only one will get him. The other four will miss out and will have to settle for a man of lesser quality. This is bad for the females.
This leads to an argument for multiple spouses that is analogous to the way free market capitalism motivates producers to improve technology and quality. By allowing a man to have multiple wives then the best man gets more women. Under the system of monogamy we have at present a man may think: "Females make up 52 per cent of the population. Therefore, if all males other than me get married then there will still be leftover women for me. Therefore, there is no incentive for me to improve myself to make me more attractive for women." Because of this lack of incentive for self-improvement men will not bother because they are rather sure they will get a wife. However, if 10 per cent of men take 80 per cent of women then this will put pressure on males to improve their quality, which benefits women because average male quality will increase. The aformentioned analysis assumes that females cannot have multiple wives while men can and if this assumption is taken out then I don't know what will happen.
Another argument against polygamy goes as follows: "The problem with to much freedom is that we become the Romans. The reason that a country (you mention the United States) becomes powerful is because its citizens have certain beliefs, in the society, in the dreams and beliefs of that society and so on. When this faith weakens the country becomes weak. For example, in Rome, to avoid military service, many citizens amputated minor body parts. This weakened the army and the whole of the empire. To much freedom does not always mean that the government has given you more rights. But that your own attention to the responsibilities that you should be assuming has become lax. There is a difficult balance between a happy population and the ability of that population to maintain the conditions that allow that happyness." To summarize this rather long argument I think it says too much freedom given to individuals may weaken the country because an individual may choose to better himself at the expense of the whole. This "responsibility that you should be assuming" is the idea that an individual should sacrifice himself for the state, as was the mantra in communist states. This analysis assumes that what we are interesting in is a strong country. If we were to take this to the extreme then the maintain a strong country it would be optimal to exterminate senior citizens who don't do anything. They don't provide any benefit to the country but they do have health care costs. Furthermore, disabled people also would need to be exterminated. It would be their duty to give up their lives for the improvement of the country. Whether you believe that an individual should be sacrificed for the state or whether the state exists to protect the individual is a matter of personal opinion with me being for the latter but let me say that one of the U.S. creeds states that each individual has rights to "life, liberty, and persuit of happiness."
Another question that comes to mind is whether having multiple wives or husbands does anything to harm the state. How does having multiple spouses make a country weaker? If anything it might make the country stronger. Suppose each soldier has multiple wives or husbands. Then they are constantly refreshed with fresh supplies. They alternate between spouses. This keeps the soldiers happy and they fight well. Of course an argument may be made the other way, that bringing too many spouses together may lead to arguments, which may stress out the soldiers.
The way I think about marriage is the same way I think about employment. When you date someone you are going through the job interview. Marriage is an employment contract. It involves an exchange of services, whether it is sex, car cleaning, housework, income, love, or whatever. Imagine if a law stated that each firm can only hire one employee. Can you imagine how bad that would be? What if you needed more? What if you owned a taxi company and you needed one-hundred drivers instead of one? What if you were a wife whose sex drive demands one-hundred husbands instead of one? She may demand a certain amount of semen per minute, say 5 liters per hour but one man will find it very difficult to produce that amount just as one taxi driver will find it very difficult to drive around say 500 people in one hour.
Another person said to me, "If you want multiple wives, why don't you move to the Middle East?" On the surface this makes sense. I want multiples wives. In the Middle East they allow multiple wives. Therefore I should go to the Middle East. However, although I want multiple wives that does not imply that I only want multiple wives. There are other things I want as well, such as proximity to relatives and friends. Being in the Middle East puts a distance between between them and me. The comment however did give me an idea. If I wanted to marry multiple wives then I could gather then up, fly to whichever country allows me to have multiples wives, and then fly back, although when I fly back I will probably only be allowed to bring one of my wives back. To visit my multiple wives I'd have to fly back and forth. I could live permanently in the country that allows polygamy but like I said there are friends and aquantances here that I need to visit.