Discrimination is unequal treatment based on a protected class, such as race, religion, national origin, sex, or sexual orientation. The Equal Employment Opportunity Commission has information about discrimination as it applies to employment situations at www.eeoc.gov. Employment discrimination isn't an issue here, of course, but that will give you an idea of how employers think of discrimination in general.
Your employer may be concerned that if only some customers are asked if they want to sign up for promotional e-mails and receive a $5 coupon, that could end up having a discriminatory impact. For example, if it turned out that only women were being asked about this opportunity and no men, a man might think that he was being discriminated against. By requiring that department store workers ask everyone to sign up, there can't be an inadvertent discriminatory impact on any protected class.
With respect to an invasion of privacy, if the company required that people sign up for promotional e-mails and give their e-mail address, that would be an invasion of privacy. However, when a customer has the choice of sharing their information and receiving a payment in the form of a coupon for doing so, or he or she can chose not to, the customer decides whether or not personal information is shared. Therefore, although private information is obtained, it is done so with consent.
Thank you for asking JustAnswer for assistance.
I can't think of any discrimination laws the situation you are describing would violate, but I can think of some consumer protection laws in some states that could be at issue.
What state are you in?
I just checked Wisconsin's Consumer Protection Laws, which are available here if you are interested: http://www.datcp.state.wi.us/cp/consumerinfo/cp/cp_laws/index.jsp.
I can't find any Wisconsin law that would be violated by not asking every customer to provide their e-mail in exchange for a $5 coupon. However, I am only licensed to practice in California. I am going to "Opt Out" of your question so that another JustAnswer expert can review your question.
Anne's answer regarding discrimination is accurate. Although I undertand the employer stated the reason a person needs to ask is due to "discrimination," that does not mean that is the only reason. In fact, many states make it illegal for a store or any business to send unsolicited emails to consumers and, by asking the consumer to "sign up" (and giving them a coupon when they do so) is a way to get a consmer to give them "consent" and avoid being charged with sending unsolicited emails.
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