What should int compareTo() return when the parameter string is null?

Question

It is said that when input parameter is null, compareTo() should throw a NullPointerException. However, I am implementing a class which needs to compare fields with the type of String. These fields need not to be mandatory. I wonder in this case,

1) What should I return when the input is null? Should any not-null strings lexicographically bigger or smaller than null?

and

2) If this is considered bad practice, is there any supporting arguments? Should I force the user to use empty strings instead? If using empty string, won't that confuse the case in which the field is not applicable and the case in which the field is empty? And if exception must be thrown, then except from warning the user in the manual, what else could/shall I do?

EDIT: I might not express myself clearly here, but in the program I am implementing, the strings that could be null are all fields or a class, which should not be null. In other words, the objects comparedTo() uses could not be null, just their private fields could be. So in this case, I believe if I implement compareTo() properly, it would not violate the transitive requirement since classes with null fields would be considered the same always. Am I right or am I interpreting this wrong?

Thank you all for the answers!

Answer 1

From javadoc for Comparable

Note that null is not an instance of any class, and e.compareTo(null) should throw a NullPointerException even though e.equals(null) returns false.