Is it too late to call for a union election?

Q. Someone from outside our company approached our HR vice president wishing to discuss a “personnel matter.” During the meeting, he presented the vice president with a set of union authorization cards signed by over half of the company’s employees. As the vice president flipped through the authorization cards, the individual stated that he is a union business agent and that his union represents a majority of an appropriate bargaining unit at the company. Are our employees entitled to an election to determine if they will be represented by the union?