I would imagine that you answered these questions in descending magnitudes of responsibility, so that as the number of people increases, you are less likely to hold authority figures responsible. I would also guess that you are more willing to hold a parent responsible for their child's behavior because you believe that the intimate relationship of a parent (1 to 1) holds more power than a baseball manager (1 to 25) or a CEO (1 to 1,000). We might call this belief, "Impactful Intimacy" since it's implied that a closer degree of intimacy is associated with a greater ability to shape behavior and thus affect the future outcome of events.
Now take a look at these questions:
How much responsibility does a baseball manager have for the team's performance?
How much responsibility does a CEO have for the success of the company?
How much responsibility does the president have over the country's economic performance?
In these questions the collective actions of people are described as a singular entity (team, company, country). It sounds much more likely that a CEO should bear responsibility for the performance of the company than to say that a CEO bears responsibility for the individual performances of all 1,000 employees, and yet they are essentially saying the same thing.
While you may have answered the initial questions by choosing less and less responsibility as the numbers increased, typically people don't behave as if this were true. When a baseball team is doing poorly it is common practice to fire the manager. This same logic gets extended to CEO's of large companies, as well as to the President of the United States, such as in the case that when the economy is doing poorly, some people act as if the president is to blame. If we are talking about the world economy, in which the United States takes part, we are holding a single individual responsible for the interactions of around 7 billion people. Even though it is often stated that the US president is the "most powerful person in the world" it is unlikely he/she can have much effect on the overall performance and behavior of the 318,900,000 million Americans, much less the economy as a whole.
Recently in the news, the president of the University of Missouri is being held at least partially responsible for the actions of students on campus. This can be framed in two ways. The first is to say that the president is responsible for the cohesion of the student body, which sounds somewhat reasonable. The second is to say that the president is responsible for the interrelations of 25,000 individuals, which sounds less reasonable. This presents us with an interesting problem.
When we are dealing with raw numbers, we may be less likely to hold leaders accountable for groups of individuals, and yet, when those same individuals are translated into concepts such as (team, company, country) we may be more likely to substitute the 1 to 1 intimate relationship that a parent has with a child, and so we assign the authority figure in those situations more responsibility over the outcomes, regardless of their ability to actually change the direction of future events. The expression "student body" is an even further metaphoric reference to this effect, as it invokes the image of a singular human body in place of the 25,000 people that it is supposed to represent.
This substitution provides us with a concise narrative, one with easy to recognize characters, a clear path of causality, and a direct correlation to "who's responsible". Instead of having to deal with 25,000 individual entities with their own desires, concerns and personalities, we simplify the situation by dealing with two characters, the student body and the president. Unfortunately, this narrative may be more in service of providing us cognitive ease than in actually explaining what is happening.
It seems when trying to determine authoritative responsibility, we are torn by two well founded conflicting fears. The first is the fear of exploitation, that if we give our leaders the slightest rationale to avoid responsibility for their actions, they will use it to exploit us for their own personal gain. The second is the fear of misperception, that by overestimating the effect our leaders actually have, we are failing to see the true causal nature of events, and thus, are doomed to an incoherent view of how the world actually works.
As we find ourselves constructing narratives that have clear causal explanations for events that spring up, such as the conflict at the University of Missouri, we should stop and reflect upon how we are framing these problems. This is much easier said then done. I struggle with the same biases of judgement as everyone else. It does help though to slow down and spend time mulling things over, writing about them or discussing them with friends. We should be willing to take both views, to be able to look at the raw numbers as well as take into consideration the unifying concepts such as team, company and country, that provide human-like qualities to abstract entities. Through this process I believe we can reach a more rational position of holding our leaders appropriately responsible, which should lead to more effective institutions and a better ability to gauge what is actually going on.