What is an organizing approach used by labor where employees sign a card of support if they want unionization, and if 50 percent of the work force plus one worker sign a card, the union considers it a victory?

Card check (also called majority sign-up) is a method for employees to organize into a labor union in which a majority of employees in a bargaining unit sign authorization forms, or "cards", stating they wish to be represented by the union.

if 50 percent of the workforce plus one worker sign a card, the union considers it a victory? Yes

Explanation:

the unionization process is:

The process of organizing the employees of a company into a labor union which will act as an intermediary between the employees and company management. In most cases, it requires a majority vote of the employees to authorize a union.

Authorization Card Law and Legal Definition. An authorization card is a form signed by an employee to designate a union as his or her bargaining agent. ... If the union gets cards signed by 30% of the employees in an appropriate voting unit (i.e. within a store), it can petition the NLRB for an election.