Support for that assertion has been anecdotal, since there is no central database of arbitrations. But by assembling records from arbitration firms across the country, The Times found that between 2010 and 2014, only 505 consumers went to arbitration over a dispute of $2,500 or less.

Verizon, which has more than 125 million subscribers, faced 65 consumer arbitrations in those five years, the data shows. Time Warner Cable, which has 15 million customers, faced seven.

One federal judge remarked in an opinion that “only a lunatic or a fanatic sues for $30.”

Daniel Dempsey of Tucson admits he might be both. He has spent three years and $35,000 fighting Citibank in arbitration over a $125 late fee on his credit card. Mr. Dempsey, who previously worked in Citi’s investment bank, said the erroneous charge ruined his credit score, and he vowed to continue until he was awarded damages.

The odds are not in his favor. Roughly two-thirds of consumers contesting credit card fraud, fees or costly loans received no monetary awards in arbitration, according to The Times’s data.

The Supreme Court’s rulings amounted to a legal coup for a group of corporate lawyers who figured out how to twin arbitration clauses with class-action bans. The lawyers represented clients that had paid billions of dollars to resolve class actions over the years. The lawsuits, companies said, were driven by plaintiffs’ lawyers who stood to make millions of dollars. They said they had no choice but to settle even those cases that were without merit.

“These lawsuits were not about protecting consumers but about plaintiffs’ lawyers,” said Duncan E. MacDonald, a former general counsel for Citibank who was part of the group. “These were nuclear weapons aimed at companies.”

Consumer advocates disagreed. A class action, they argued, allowed people who lost small amounts of money to join together to seek relief. Others exposed wrongdoing, including a case against auto dealers who charged minority customers higher interest rates on car loans.