Have a gander at Language Log where the “singular they” has been extensively discussed—mostly, apparently, because it’s something of a litmus test to determine whether someone is a descriptivist or a prescriptivist grammarian; the LL crowd falling squarely in the descriptivist camp.
The short answer is that it’s grammatically plural; it’s a “plural of indeterminacy of number” primarily, and has taken on under social pressure an aspect of “plural of indeterminacy of gender”. Number one is correct.
Have a gander at Language Log where the “singular they” has been extensively discussed—mostly, apparently, because it’s something of a litmus test to determine whether someone is a descriptivist or a prescriptivist grammarian; the LL crowd falling squarely in the descriptivist camp.
The short answer is that it’s grammatically plural; it’s a “plural of indeterminacy of number” primarily, and has taken on under social pressure an aspect of “plural of indeterminacy of gender”. Number one is correct.
ETA: background info.