Any definition that excludes the possibility of polygamy within a family unit falls short.
The argument
A sociological definition of the family has to describe families as they exist rather than as one society imagines them, and the cross-cultural evidence posed a problem for any definition built around a married couple. In his work, George Peter Murdock found that 195 societies in his sample were non-monogamous, while only 43 were comprised of monogamous couples. On those numbers non-monogamy was not a deviation from the human norm but closer to the norm itself, and monogamous pairing was the minority arrangement. A construct that took the monogamous couple as its starting point would therefore have failed at the first task a sociological concept has to perform. It would have classified the majority of the societies being studied as lacking families altogether, which is plainly the wrong result. Any definition meant to travel across cultures had to reflect the prominence of polyamory rather than treat it as an exception to be handled later. This is what the definition by shared residence, economic cooperation and reproduction was built to accommodate. Each of its three criteria describes something a household does rather than who is married to whom. People living under the same roof, pooling labour and resources, and producing and raising children between them satisfy all three regardless of how many sexual partners are involved or how those relationships are formalised. A household in which multiple partners live together and take part in domestic responsibilities counts as a family on this definition exactly as a monogamous one does, because the definition asks what the unit does rather than what shape it takes. Defining the family by function rather than by marital form is thus not a loosening of the concept but what makes it usable across the range of societies in which families are actually found. Because polyamorous and non-monogamous relationships are widespread, family is best understood as a shared residence, economic cooperation, and reproduction.
Context
Any sociological definition of a family must be able to accommodate the ubiquity of non-monogamous relationships across cultures.
Premises
Counter-arguments
Critics reply that Murdock's cross-cultural data establishes only that monogamy is not universal — not that his particular 'shared residence, economic cooperation, reproduction' definition is correct. The prevalence of non-monogamy is evidence about marriage forms, not a validation of these three criteria. They add that the definition's inclusion of reproduction excludes childless couples, adoptive families and same-sex families widely recognised as families, and that it centres a dated functionalist model. Modern sociology increasingly defines family by relationships and function — 'what families do' — rather than a fixed checklist of residence, economy and reproduction, so Murdock's construct is contested.
Rejecting the premises
[Rejecting P1] Murdock's sample showing many non-monogamous societies establishes that monogamy isn't universal, not that his residence-economy-reproduction definition is correct. [Rejecting P2] Including 'reproduction' excludes childless, adoptive and same-sex families widely recognised as families, so the definition fails to capture arrangements it should. [Rejecting P3] Modern sociology increasingly defines family by relationships and function ('what families do') rather than a fixed checklist, so Murdock's criteria are dated and contested.