The bystander effect describes a phenomenon where diffusion of responsibility leads to inaction.
There is an infamous parable, a now-classic staple in psychology classrooms across the country, about Kitty Genovese — the woman who was supposedly murdered in Queens in front of dozens of onlookers who failed to do anything to help, each person assuming that the other bystanders would assume responsibility.1 This phenomenon is known as diffusion of responsibility or the bystander effect. Essentially, the larger any group gets, the less likely it is that any single person in that group will intervene or take action when confronted with any given situation, because each individual sees more other people around who could take responsibility or “pick up the slack,” so to say. (html)
The broader issue of diffusion of responsibility is studied in Normal Accident Theory.