The primary advantage to monogamy is social acceptance, which would seem to be a bit of a wicked cycle; were people less afraid of social rejection, there may be a rise in polygamy, if there is a rise in polygamy, it would become more socially acceptable.
Other than that, there is the matter of legal marriage throughout various countries in the world. Many countries, even those which allow homosexual marriage, do not sanction polygamous relationships in the least, much less allowing marriage to multiple people.
There is also the point of less exposure to anything sexually transmitted, though this would be more an advantage of honesty and communication within a relationship.
As well, there is less of a chance of jealousy between the members in a perfectly monogamous relationship, though, again, this may be averted through honest communication and expressing one's comfort levels.
Honesty and trust should be enough to make any relationship work, monogamous or not, and thus the only advantages to a monogamous relationship would seem to be those imposed upon us by society and individual preferences.
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Monogamy means the practice of having only one wife
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not sure need help too.
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