What is the impact of showing the amount of unattended notifications to the user? What is the difference in cognitive effects on the user between simply showing that there are 'some' unattended notifications, or showing how many notifications there are?

Take Facebook's notification count for example, 


as opposed to Windows' PC issues notification  in the system tray.

Of course depending on what the notification is notifying you of, people will respond differently, which is not something I'm interested in. However, I suspect there could be a difference based on where it is being displayed, e.g. whether it  is always visible or not. Would one be preferred over the other in different situations?

I'm mainly interested in a comparative study between the two, but any research which might give additional insights in the two separate representations would help me out as well.
For me it is the inference that the more notifications I have the more value I will have in bothering to click it.

That 1 notification on a social networking site might be a request to play some terrible game.. however 24 notifications are likely to yield at least something beneficial for me to justify having bothered clicking it.

The higher the number the increased urgency I feel to check them (maybe the same person is repeatedly trying to make contact and I am unintentionally ignoring them!).

As for there being a notification with no number, that is easier for me to ignore. In the case of the Windows' PC issues (Action Center) in the task-bar, there is always a notification in it for me, so I have learnt to dismiss it.. I have become de-sensitised to seeing that alert. If however the icon increased in number and I detected this change, then I would deem that to be an increase in urgency and would be more likely to click it again.

I think if I kept clicking Action Center and felt it yielded little value to me then I would be able to filter out if the numbers were to keep increasing, but I would find it more difficult to ignore and feel tricked by it just in-case this new state meant something important this time round..