‘He or she’ versus ‘they’ - Oxford Dictionaries Online

This article describes several gender-neutral options to the outdated, sexist use of pronouns like he and him to refer to both men and women. It also comments on the issue of using plural pronouns to refer to singular nouns.

The article says:

It’s often important to use language which implicitly or explicitly includes both men and women, making no distinction between the genders. This can be tricky when it comes to pronouns. ... There are no personal pronouns that can refer to someone (as opposed to something) without identifying whether that person is male or female. So, what should you do in sentences such as these?

One of the choices is to use plural pronouns like they and them instead he or him -- even though the pronouns refer to a singular noun:

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The article concludes:

Some people object to the use of plural pronouns in this type of situation on the grounds that it’s ungrammatical. In fact, the use of plural pronouns to refer back to a singular subject isn’t new: it represents a revival of a practice dating from the 16th century. It’s increasingly common in current English and is now widely accepted both in speech and in writing.

Here's what my online resource -- Garbl's Editorial Style Manual -- says about that issue (with links to other related advice):

their, them, they The day may come--and should--when these plural pronouns are accepted as singular pronouns that don't note a person's sex. Some respected writing authorities now suggest this change in language as we eliminate the outdated use of he, him and his as references to both men and women. This updated usage would be similar to use of the pronouns you and your for both one person and more than person, taking a plural verb even when mentioning one person.

Still, for now, consider the potential reaction of your audience--and the reaction you would prefer as the writer or editor--before applying this use. Meanwhile, try other acceptable uses, especially using the plural pronouns to refer to plural nouns. See he or she, he/she; his or hers, his/hers; pronouns; sex, sexism. 

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This article is featured in today's (July 20) Garbl's Style: Write Choices -- available at the Editorial Style tab above and by free email subscription.