Early Dynastic texts are difficult at the best of times, and this one is no exception. However, the idea that polyandry is being described here is most likely a misunderstanding.

Prof. Claus Wilcke (2003:160, 2007:59) translates the passage as "It was so that women of former times took two husbands each. Today’s women have abandoned that crime." However, his interpretation is that this is about marital separation and remarriage. Divorce was expensive and required a payment in silver, a fee to the commissioner, and the extrication of the wife's dowry from her husband's property. Therefore, he believes this refers to Iri-kagina.k claiming to have ended the practice of remarriage by separated but not divorced women by making divorce more accessible.

An alternative translation is provided by the late Prof. Douglas Frayne. His is as follows: "as for women of former times – a man (could) take two of them; but for women of today – indemnity payments have been removed (and the practice has been abolished)." (2008:273). This is very different. It seems to be a ban on polygyny.

I'll provide the transliterated text (from Frayne) to illustrate the difficulty.

20') munus u₄-bi-ta-ke₄-ne

21') nita 2-ta

22') ì-tuku-am₆

23') munus-u₄-da-e-ne

24') za-áš-da-bi ì-šub

The main source of difference arises from line 21, nita 2-ta. Nita is male, easy enough-- but 2-ta means something like 'two each'. Thus we might read:

20') [regarding] women of former times,

21') two each a man

22') could marry.

It's not easy to interpret this. Further complicating our attempts to establish what conditions were like on the ground, law codes such as these are sometimes best understood as works of literature rather than accurate descriptions of the laws that were practiced and enforced and the problems they actually solved.

There is no evidence for polygamy in Early Dynastic sources, though as during the Sargonic period female slaves could probably be taken as concubines with the wife's permission, especially if the wife could not produce children. Later on, monogamy was the rule for the people, though kings and other high-ranking figures might have many wives.