What is rule and constraint on polygamy and polyandry in Jewish law? Are they allowed or prohibited? In both cases--whether allowed or not--give me the sources.
I found one or two questions on polygamy, but no one discussed polyandry.
There are commonly two answers given as to why its ok for a man to marry multiple wives, but not ok for a women to marry multiple husbands.
Since tribal affiliation is determined by the father, and eventually land distribution as well, it would create a conflict since you can never really be sure who the father is. However, you should seemingly always know who the mother is.
There is a theory that the only reason why a man is allowed to marry two wives in the first place, is so that there is a method for society to take care of women, who otherwise would not be able to get work and be cared for. Since it is assumed that a man can get along as a single person just fine in society, there is no reason for a woman to marry an extra man. Except for orphans, or the extremely poor or sick, there is no special commandment to take care of the Widower. However, there is a commandment to take care of a widow.
2a. (Kabbalah) By the nature of the way that humans pro-create, a Woman is designated as a "receiver" (egg) and a man is designated as a "giver" (sperm). In marriage, this is also true, and the man is obligated to give and take care of his wife, however a wife has no similar obligation to her husband. A woman having two husbands, would seem to be a situation where you have the "receiver" being in the dominant position of who can "give", and would thus be a distortion of roles, similar to the prohibition of a woman not being allowed to wear men's clothing and visa versa.
In terms of polygamy, see the answers to this question: Questions about Polygamy in Jewish Law and Culture