Which power involves the authority to interpret the laws and to settle disputes between members of society?

The Judiciary Branch of the U.S. Government has the power to interpret the laws and to settle disputes between members of society. The American Judicial Branch includes a system of courts that range from the Supreme court, to Federal courts across the country, to state/city courts, and also civil courts. All of these courts form the American Judicial system or the Judicial Branch of Government which interprets the laws and calls for their enforcement.