The question was put: "What are the pros and cons of polygamy?"
To which I responded:
It seems to me that the bulk of the criticism of what has erroneously been termed "polygamy" is really about non-egalitarian polygyny (one husband having multiple wives).
My position on the subject, which I have held for years now, is that both polygyny and polyandry should be legal, with the following conditions:
1. There must be capacity (persons who have a mental disability or who have not reached adulthood cannot competently agree to enter into such a relationship);
2. There must be informed consent, meaning that all partners must be aware of the arrangement before their consent to it is deemed valid;
3. The consent must be given in the absence of coercion or duress (including coercion exerted through the cloak of religious authority or position, i.e., a flaming angel told me this is what God commands, etc.);
4. There must be laws in place protecting the human rights and property rights of those involved, including children, so as to prevent abuse, neglect, etc.;
5. Individuals within the polygynous/polyandrous family must be free to terminate the relationship if so desired, with the condition that the divorce laws pertaining to such termination account for the continuing needs and responsibilities of the parties (i.e., alimony, child support, etc.).
In evaluating the pros and cons of polygyny as called for in the question, it is critical that we distinguish between coercive/non-egalitarian relationships and those entered in situations meeting the above criteria.
In non-egalitarian arrangements (which I consider deplorable and which should remain illegal the world around), there are admittedly some benefits which may flow, both to the women and the men. Many of these have been mentioned- comradery among wives, more sex for the man, built-in babysitters, pooling of economic resources, specialization of talents and abilities, etc. But the detriment is that we do violence to our human dignity, and elevate the man's worth and status above the women. Where polygyny may be coerced, especially in heirarchical religious societies, many men will also be excluded from the possibility of ever having an intimate relationship or marriage. And the women in the polygynous relationships will be oppressed and forced to accept circumstances which they did not voluntarily consent to.
But in the egalitarian setting, it is a whole different ballgame. If two men want to marry one woman, then they have little right to complain that she is unavailable for sex when she is intimate with the other one, because that is what they signed up for. Likewise, women who truly consented to a polygynous relationship are simply getting what they signed up for when they get less total attention from their husbands because he is spending time with one of his other wives. I believe that mature adults have to moral right to consent to whatever responsibly practiced marital arrangements they wish, with the conditions above, and neither God nor man should prohibit it. There may very well be diminished intimacy in a multiple-spouse situation, but it is up to individuals to decide whether that is something they can live with.
Come to think of it, it is rather strange that people would bother to debate the pros and cons of truly consensual polygamy among non-coerced adults, at least to the extent that it does not involve children and property rights. The sex/relationship aspects ought to be a no-brainer: of course it's fine in the egalitarian context! Those women or men who would not want to share a spouse need only refuse to enter into one of those relationships. Those competent, consenting adults who would be willing to share a spouse, on the other hand, of their own free will and choice, ought to be able to do so generally, and it is not any of our business to tell them they cannot.