Here's the situation: Both alternatives are incorrect; but you have to choose one.
In 1982, I published my first book, Victim: The Other Side of Murder. The story chronicles a family of six, two of whom had been trapped in the basement of a hi-fi shop at the mercy of a mass-murderer. The book was the first work of narrative nonfiction to illuminate the victim’s side of violent crime. I dedicated it to my parents and to the surviving members of the family who had bravely opened up to me. But in expressing my gratitude, I faced a problem: three members were men; the other was a woman. After I had struggled for many hours, that half of the dedication finally read:
The story itself
Belongs to the Naisbitt family,
And I am indebted to each of them
For sharing their part of it with me
Even though each is singular and their is plural, I saw no other solution. Fast forward to last fall, when I wrote a tip about forming possessives and how polite society in the early eighteenth century did not tolerate inanimate objects possessing things. I included this clause:
. . . so anyone caught writing ‘the ship’s mast’ could find themselves not invited to the next garden party.
One of your colleagues, Jerry, wrote that he found it interesting that I had “fallen prey to using the third person plural as a generic pronoun.” He means that anyone is singular, yet I refer to it with the plural pronoun, themselves. If Jerry had read the dedication in Victim, he would have said that each is singular and their is plural, so they don’t agree either.
I could have written “each . . . for sharing his or her part” and “anyone caught . . . could find herself or himself not invited.” But neither is a good alternative. I also could have gone with the royal he and cut out half of the planet’s population: “for sharing his part” and “anyone caught . . . could find himself not invited.”
The third person singular pronouns are:
she, her, herself, he, his, him, himself, it, its, and itself
The third person plural pronouns are:
they, them, their, and themselves
The indefinite pronouns include:
anyone, everyone, no one, someone, each
There are more, but you get the point.
TWO PROBLEMS THAT OVERLAP
The First Problem
In the eighteenth century a group of grammarians arbitrarily decreed that indefinite pronouns should always be singular and require singular verbs: anyone is, everyone is, no one is, someone was, each has been.
The Second Problem
The grammar decree hit an especially hard stonewall when the grammarians tried to match the singular indefinite pronouns to the singular third person pronouns. You can imagine the angst when someone tried to post an ad in the Boston Bugle:
Anyone attending the candle-making class must bring ____ own wax.
Is it her, or is it his? That was the dilemma: If we used the plural their with the indefinite anyone, we would be wrong because anyone is singular, and if we used her or his, we would be equally wrong, because one does not include the other. Merriam-Webster’s Concise Dictionary of English Usage calls these two problems “perceived gaps in the language.” And the gaps intersect right at this point: in English we have no singular third person pronoun that covers both women and men.
A THICKER PLOT
Up against that stonewall, the eighteenth-century grammarians pondered, If anyone is singular, and we have to match it to a singular third person pronoun—but we don’t have one that means both genders—can we match it by decree to her or his anyway? Of course they could, and as shocking as this might seem, they decided on the masculine his (he, him, himself). Can you imagine? It might have had something to do with all of the grammarians being men. Some writers followed this practice so rigidly over the next two hundred years, they produced sentences like this one from a New York politician in 1984:
“. . . everyone will be able to decide for himself whether or not to have an abortion.”
But going back to the fourteenth century, writers and some grammarians faced with the dilemma were already using and continued to use the plural they, them, their, and themselves to refer to the indefinite pronouns. “And every one to rest themselves. . . ,” wrote Shapespeare in The Rape of Lucrece, 1594. “I would have everybody marry if they can do it properly,” opined Jane Austen in Mansfield Park, 1814.
As much as we try to make language like math, with strict rules and predictable outcomes, doggone it, it just won’t stuff in properly. Faced with Shakespeare, Austen, Lord Byron, and other literary luminaries, grammarians went back, pondered some more, then rationalized: although indefinite pronouns might not be actually plural, they are notionally plural.” And everything was fine again.
Although a few critics disagree, I would not hesitate to use the plural they, them, their, or themselves to refer to a singular noun of indeterminate gender (writer, laborer, secretary, nurse, governor) or an indefinite pronoun, as I did in my book in 1982. And the next time someone questions your doing that, look down your nose and sniff, “Haven’t you heard? Indefinite pronouns are notionally plural.” Then duck really low.