You are correct and also inaccurate. If there are 500 grad students, 250 of them can say "we wanna organize" and poof they're in the union. Or, if there are 500 grad students, 150 of them can say "we wanna organize" and now there's a vote. The union and the "employer" get to fight about who's allowed to vote and when the vote happens and yeah - if only 40 vote, 21 "yes" votes means you're union. But if only 40 people voted and the employer has made it abundantly clear he'll fire anyone who voted "yes" if the union measure fails, then you can consider that to be 460 votes for "yes", 21 votes for "hell yes" and 19 votes for "I'm a toadie who was bought off." When dealing with employment one cannot disregard coercion.A petition can be filed by any union, worker, or employer. Workers or a unionmay request an election if at least 30% of workers have signed a petition or authorization cards (i.e., cardsauthorizing a union to represent them).