The correct answer is C. their. Will each of the candidates share their thoughts? You should avoid using phrases such as "his or her' because there is a better pronoun to denote both genders - and that is 'they.' So it is more economical to refer to a candidate whose sex you don't know as 'they' so as to avoid any confusion. If you need to clarify the exact gender, then you will use the appropriate pronoun. You cannot use 'theirs' here, because that word is not followed by a noun, and here, the word 'their' is followed by the noun 'thoughts.'
