“They shook their heads” or “They shook their head”?

Should one say they shook their heads in disbelief or they shook their head in disbelief? The first kind of conjures up many-headed people? Similarly should one say they referred the question to their husbands/husband?

Solution 1:

The earliest instance of "shook their heads in disbelief" in a Google Books search covering the years 1700 through 2008 is from 1871. From "Sparks from the Village Forge," in The Shamrock, volume 8 (March 1871):

The magistrates whispered again : and shook their heads in disbelief. The old man was wanting to save Mark, they said. The truth was, however, that he was, when the note arose, in that reverie of memory, which laid its spell upon him when his eyes looked over the land and saw only vanished scenes.

The most recent is from 2008 (the last year included in my search). From Karen Linamen, Due to Rising Energy Costs, the Light at the End of the Tunnel Has Been Turned Off (2008) [combined snippets]:

But now I'm forty-six. So when my folks came into the kitchen and shook their heads in disbelief at all their gyrating offspring, in-laws, and grandkids, well . . . what could they do? Send me to my room? Actually, they may have shaken their heads in disbelief, but they were smiling at the same time.

Altogether, the Google Books search turns up 84 matches for "shook their heads in disbelief" during the search period and 0 matches for "shook their head in disbelief." So in published writing there appears to be a strong preference for the former phrase over the latter. This not to say that "shook their head in disbelief" is wrong, or that the preference in writing carries over to speech (since I'm not aware of any objective basis for making that claim). But if you are writing something and the phrase "shook their head/heads in disbelief"comes up, you may be interested to know that the preponderance of usage is unmistakably on the side of the plural heads.

The preference for "their husbands" over "their husband" in a Google Books search for the period 1700–2008 likewise shows a clear preference (in writing) for the plural form. Here is the relevant Ngram chart matching "their husbands" (blue line) against "their husband" (red line):

The support isn't unanimous, but it is pretty strong. Going forward, I would expect the split for "their spouses" versus "their spouse" to be less clear-cut because the modern use of they as a gender-neutral singular pronoun is likely to yield occurrences involving "a married person" and "their spouse"—a situation where TimLymington's test question "Did they have one spouse between them?" would be answered in the affirmative.