In the late 1800s, why might a potential new factory employee refuse to sign a yellow-dog contract

The answer is: because signing yellow dog contract would strip the employee of his ability to protest workplace injustices with the support of an organized workers' group

Yellow dog contract refers to the type of contract that made to prevent employees from joining worker's union. When workers were not in a union, the likelihood of them able to join their effort to discuss better working condition would dramatically diminished. This will give a great advantage for the e,employers.

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