Interesting thread!
Firstly, I think people are getting confused about who's 'declaring an emergency'.
Pilots have three choices: None, PAN or MAYDAY.
These purely indicate to ATC (and other a/c on frequency) the desired priority the pilot wishes to receive, and I guess means ticking a different box in the subsequent pilot's report.
So that could be termed 'declaring the desired priority state' rather than declaring an emergency.
From ATC's piint of view, we have to decide the level of emergency response, and we have perhaps ten different levels, each tailored towards a certain seriousness and time scale. We have 'Aircraft Accident Imminent' for a twin that has a double engine failure at ten miles out. We have a Full Emergency which we are required to put on for an a/c landing with 50% or more of its power out. All the way to a 'Local Standby' which means that the firefighters stop playing snooker and roll the doors of the fire station up - this could be for a 747 coming in with one engine out, or might be precautionary due to strong crosswinds. Many of our responses are mandatory (50% power loss, any type of hydraulic failure etc).
So rather than declaring an emergency, we are 'declaring the response state'. Can we not get bogged down again in the semanitcs of the word 'emergency', and who declared it first!
We don't wait for a tug driver to declare a MAYDAY before responding.
Winston. It all depends on the timescale. After you sorted yourself out and let us know the problems you were having and when you were returning, we'd decide to put on a Full Emergency at the least (50% power loss). This would depend on your ETA, as there's no point in getting people out there to wait for an hour as you dump fuel. If you subsequently went back to a PAN, all that indicates to us is that you've decided you're not in as great immediate danger, but the underlying reason for our response is still there (no engine), Once we have promulgated a type of response, it is for either the Chief Fire Officer, or Chief Police Officer, to downgrade the response, not even we can do it.
Again, whether you say PAN or MAYDAY has no immediate bearing on what hospitals do. At Heathrow, if we declare a Full Emergency, then London Ambulance Brigade and London Fire Brigade do attend, so they have to reposition assests from elsewhere to cover those at the airport. They don't start tipping patients out of beds!
Declare a MAYDAY or PAN to get our attention, then talk the problem through with us, and if we have any discretion, we can decide what response is appropriate.