Question

everybody's responsibility is nobody's responsibility expansion of idea

Answer 1

When people believe that a particular job is everybody's responsibility, no one actually takes the initiative which results in the task being nobody's responsibility.
Eg-
When we talk about stopping littering on roads, it is everybody's responsibility but no one takes the initiative to do so and it ends up being nobody's responsibility.
Basically nobody wants to take the initiative.

Answer 2

.An expansion of the idea behind this sentence could be: if the responsibility for something needs to be accounted by everyone but not somebody in particular, or not by some defined group of people in particular, then the responsibility is so diluted that it becomes nobody´s responsibility, that is to say, nobody takes ...