Polygamy refers to the practice of having more than one spouse. It is broader than polygyny, which refers to one man with multiple wives, and polyandry, which refers to one woman with multiple husbands.
Examples
It is widely assumed that polygamy denotes specifically the marriage of one man to multiple women. This is probably because polygyny is more common (or more newsworthy, at least) than polyandry. In current news sources, polygamy mostly appears in reference to North American religious sects that in fact only practice polygyny:
In 1890 the church banned the polygamy for which it used to be notorious. [The Economist]
It was during this period that polygamy was slowly being phased out under pressure from state legislators. [Guardian]
Polygamy is technically correct in these cases, but polygyny would be more precise. The extensive use of polygamy in place of polygyny has probably excised the latter word from the language (outside scientific contexts) and permanently confused the former’s meaning. Hence these writers seem to think polygamy is the opposite of polyandry:
Polyandry and polygamy, religiously authorized or mandatory, have not survived as legal institutions in the West. [NY Times]
The former Pennsylvania Senator … suggested other “consensual acts,” presumably, polygamy and polyandry, for example, were comparable to same-”‹gender sex. [The New Civil Rights Movement]
Because polyandry is a form of polygamy, these sentences are technically illogical (though, of course, we all know what the writers mean).
