OK, I am just a dumb schmoe toiling in the tech support salt mine, so I need help with a math problem to aid me in prioritizing my day.
Say that I have 10 people that need help. Of that 10, let us say that 8 of them are the most important people in the entire fucking universe, and demand that I help them first. The question: who do I help first?
I mean, the customer IS always right, aren’t they? And if all 8 of them state that they are more important than Jesus, the Apostils, Mother Mary and all of the Saints that has to be true, right? And if they are all claiming that they will explode, return the product and that life on earth will come to an end if I fail to immediately solve their lame ass problem, that has to be true right?
I tried to give the problem to the computer, but (just like in Star Trek) it caught of fire! What’s a tech-boy to do?
What, you can’t hop in the clone machine and make a few copies of yourself?
Sheesh. Amateurs.

Assume that these people use “more important than” to mean a circular relation, and help the other two.
Being a veteran of eight years of tech support at a telco, I’ll tell ya - Payroll Is Always First.
Without Payroll, nobody gets a paycheck. Even the most rabid me-firster will usually back down when faced with a “Well, would you like a paycheck sometime this month?”
Then go with the two people who haven’t felt a need to impress you with their importance. That’s because they really are, and don’t need to browbeat a mere peon to prove it. One is likely the company president, and the other is likely the owner…
Then, its Revenue Accounting. If we don’t collect money from customers, we don’t make money. If we don’t make money, us employees don’t get paid. At least, not for long.
After that, it’s whatever order you feel like doing them in. I generally go with whoever hassles me the most goes to the bottom. Unless, of course, they have a legitimate business case for overrunning support (we have priorities of our own…six people not working does override your desperate need to change your wallpaper.) priorities. Sent in e-mail format, if you please.
Then they are dumped on my boss’s desk, and it becomes HER problem.