Polygamy means having more than one spouse but, practically-speaking, polygamists are almost always polygynists: one husband, multiple wives. There’s an obvious inherent sex-based power inequality in any heterosexual polygamy; in polygyny, that power inequality is patriarchal. This is a problem in-and-of itself considering the greater patriarchal society we live in.
Now, I’m not saying there can’t be loving, respectful, fulfilling polygamous marriages; I’m just saying the inequality is there. But inequality isn’t necessarily bad. In spite of current lingo, most people in the world do support and willingly submit to some inequality.
The U.S. President, for instance, has more power than your average U.S. citizen. Even if you decry the President’s vast wealth, still, someone has to make the decisions and guide the practice, right? In a polygynous marriage, that someone is the husband.
The problem with polygamy is that the inequality is not based on individual merit but, rather, sex. That’s a big problem becuase, aside from individuality, there’s no good reason to think any given woman has less intelligence, less physical ability, less spiritual authority, less practicality of mind, than any given man. In situations like this, people become defined by an aspect of themselves they are born into and can’t change; they lose some flexibility in life, some choices are denied them; and if the fit isn’t right, they suffer and those around them suffer. This is true of both sexes. Does a man who, by character, is not a leader do a good job of leading? Does he enjoy his role? Do his ‘followers’ enjoy their roles and do a good of ‘following’? No, no, and no. The whole system collapses.
Open marriages, on the other hand, can take many forms. The only thing that defines “open marriage” to everyone is what it isn’t: not monogamy. When it comes to specifics, open marriages are defined according to the parties involved. They can be equal – both partners exercising the same rights, engaging in the same practices – or they can be unequal. Assuming both parties are being honest and sincere with themselves and each other, there’s no harm, no foul, either way (equal or unequal). That’s because the arrangement has been made based on the individual characteristics, desires, morals, of the people involved.
Positive and negative effects? With polygamy, it comes down to luck: whether or not the people involved fit their sex-based roles. With open marriages, it comes down to one’s insight into oneself and communication skills. Both systems can work out wonderfully; both can be terrible disasters. Frankly, I’d rather not rely on luck, but that’s just me.