When voters in Tacoma, Wash., and Portland, Maine, last month voted to reject ballot measures raising minimum wages in their cities to $15 an hour, it was a big win for the hospitality industry—employers and workers alike.

Many restaurant owners have warned that drastic increases in the minimum wage would force them, in an effort to keep labor costs in check, to eliminate tipping and to raise prices. That would be bad for workers, although not everyone believes so. The prominent restaurateur Danny Meyer announced in October that he will gradually eliminate tipping at his 13 restaurants in New York City. A number of West Coast establishments have transitioned away from tipping, as profiles in the San Francisco Chronicle and Seattle Times can attest. Joe’s Crab Shack, a national chain, has begun testing a no-tip policy in 18 of its locations.

Federal law permits restaurant owners to pay tipped employees a lower base wage of $2.13, so long as they earn at least the minimum wage of $7.25 when tips are included in total compensation. But a handful of states, including California and Washington, don’t allow restaurant owners to count tips as earned income, ignoring the determination of the Internal Revenue Service and their own state tax agencies. For instance, in the city of San Francisco, an employee who earns $20 an hour in tips must still be paid the full minimum wage of $12.25 an hour.

Other states do recognize tips as income but have dramatically increased the base wage that restaurants are required to pay tipped employees. In February, for example, a New York wage board appointed by Gov. Andrew Cuomo approved a 50% increase in the state’s minimum wage for tipped restaurant employees, to $7.50 an hour from $5. “When you suddenly increase the front-of-the-house labor cost by 50 percent,” restaurateur Andy Ricker explained to New York magazine, “the biggest losers in this scenario are the back-of-house employees, as it freezes or lowers the cap on what they can be paid.”

Restaurants on the West Coast have solved this problem by eliminating tips but raising menu prices or adding a surcharge to the bill to support higher pay for the rest of the staff—in effect, redistributing income away from servers. That’s great news for the cooks, but not for wait staff accustomed to nightly gratuities but now earning a flat hourly rate.

At an Oakland restaurant named Bocanova, 60% of the wait staff quit after tipping was eliminated. Bar Agricole and Trou Normand in San Francisco reinstated the practice in October, less than a year after dropping it, because they’d been losing wait staff to restaurants that allowed tips. Mr. Meyer hopes to avoid a mutiny by his employees with a new revenue-sharing program that will redistribute a share of the restaurant’s sales.

The Employment Policies Institute, where I work, commissioned Google Consumer Surveys to perform a nationwide poll of roughly 2,500 self-reported tipped restaurant employees to measure their aversion to a no-tip policy. Asked if they would agree to eliminate tipping in exchange for a guaranteed minimum wage of $15 an hour, nearly 60% said no.

Perhaps an even greater question is whether customers will adapt to life without tips—and the higher prices that such a policy means. Mr. Meyer’s team estimates that menu prices will need to rise by up to 25% to pay increased salaries and offset the absence of a gratuity. These price hikes might fly in wealthy coastal neighborhoods, but in much of the country they may leave diners with sticker shock.

Consider: At the Old Bus Tavern in San Francisco, tip-included prices mean you’ll pay $17 for a bowl of meat chili and $8 for the cornbread to go with it. At Ivar’s Salmon House in Seattle, a dinner portion of Alaskan Halibut with a side of wild rice costs $40, tip included. Lanesplitter Pizza in Emeryville, Calif., has moved to a tip-less model and serves “pizza for the people” that costs $30 for 15-inch specialty pie.

It’s perhaps too early to tell whether the tip-less policy will hurt customer service, although reviewers on Yelp are already wondering. “While the food was great, our service was next to non-existent,” one wrote of Ivar’s in Seattle. “We all wondered if this was a result of the new tips-included policy.”

Tacoma and Portland won’t be the last cities to face this decision. A new organization called the Fairness Project, backed by a powerful Service Employees International Union local in California, announced in October that it is raising $25 million to put the minimum wage on the ballot in as many states as possible in 2016. As more full-service restaurants are forced to consider the tip-free approach, the customers confronted with higher prices and employees who face smaller paydays should remember who’s to blame.