My assumption was that A, B, C have no preference other than their own favorite restaurant. If C picks up his own favorite restaurant out of X, Y and Z through blind luck (1/3 probability), then A and B have to agree upon a restaurant between A and B's choice to circumvent C's fair selection. They would be each rooting for their own favorite and won't be able to reach a compromise.
In any case, C can always demand a password protected document with the actual translation of X,Y and Z before making the choice. Once C makes the choice, then A or B can reveal the password so that C can open the document and confirm the choice made. Of course, this still leaves the option of C breaking the password if he's a master hacker or something. But I think that would be a stretch and can still be avoided by using a very strong password (encrypting) and asking C to make his choice within a minute of getting the details (so that he won't have time trying to unlock the code). They can all be online to make sure C responds immediately.