This is the week for academics to weigh in on polygamy, it seems (earlier post here). The Right Coast has a short utilitarian analysis of polygamy versus monogamy. Summary: Under polygamy (and assuming more wives mean greater utility) some men are better off and some are considerably worse off, namely those who are pushed out of the marriage market. Some women are better off (under the "half a good man is better than all of a bum" theory) and some are worse off (those women who now have to share a good man).
The obvious question (not considered in the short post at Right Coast) is why women who would be worse off under polygamy would freely choose polygamy rather than either (1) relocate to a monogamous location or subculture; or (2) make monogamy a condition of marriage. I think under free migration and full information, women who would be worse off under polygamy would exercise those options if available. This explains why Mormon polygamy persisted: In isolated Utah, women faced formidable barriers to relocation. Furthermore, in the early years, polygamy was practiced secretly so first wives were not in a position to bargain a "monogamy prenup" or think they needed to relocate in order to secure a monogamous marriage. There's always the possibility that women entering marriage in an openly acknowledged polygamous subculture might nevertheless naively believe that their husband, basking in the fulness of monogamous bliss, would decline the option of pursuing additional wives. Marital choices are not, I think, the best context for rational decision models.
One caveat: Generally, expanding the choice set of an individual can never make that individual worse off, so how could moving from monogamy to polygamy make anyone worse off? Think of society as a whole, then focus on those individuals who face a shrinking pool of marriage partners. They actually face a reduced choice set rather than an expanded one. So, for example, while wife no. 4 and her polyg husband might be marginally better off (assuming wife no. 4 prefers that choice to being wife no. 1 to the best monog candidate), the now-disappointed if less desirable monogamous suitor of wife no. 4 is now considerably worse off (assuming marriage would have increased his utility), and polygamy has lowered total social utility (assuming we can sum personal utility across individuals, a debatable but accepted practice).
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