A DESCRIPTION OF THE PROBLEM :
The example in the API Note is wrong, it doesn compile. The identity value is missing in the reduce method call.

  Map<City, String> longestLastNameByCity
         = people.stream().collect(groupingBy(Person::getCity,
                                              reducing(Person::getLastName, BinaryOperator.maxBy(byLength))));

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
  Map<City, String> longestLastNameByCity
         = people.stream().collect(groupingBy(Person::getCity,
                                              reducing("",Person::getLastName, BinaryOperator.maxBy(byLength))));
ACTUAL -
  Map<City, String> longestLastNameByCity
         = people.stream().collect(groupingBy(Person::getCity,
                                              reducing(Person::getLastName, BinaryOperator.maxBy(byLength))));

URL OF FAULTY DOCUMENTATION :
http://docs.oracle.com/javase/8/docs/api/java/util/stream/Collectors.html#reducing-U-java.util.function.Function-java.util.function.BinaryOperator-