I dust first, and then vacuum. If you vacuum first, and then dust, you will get dust on the carpet again.
I dust first.
Dust so that it will settle on the floor to be vacuumed up. If you have an older vacuum that doesn't have a HEPA filter, it doesn't matter. It will release dust back into the air and you will have to dust again.
Start at the top and work my way down, vacuuming is the last thing I do.
Dust then vacuum.
Its called "Top Down" cleaning.
The idea being, you start with the higher objects or clean that which when displaced will settle. So if you had a ceiling fan, you would dust that first, then dust the next thing lower, then lower until it is time to vacuum. The idea is that if you do this, then by the time you take out the vacuum, all the dust not picked up by the duster, has settle to the floor for vacuuming.
All of the answers above I agree with.
I dust first!
Top down (dust then vacuum) works very well, especially with vacuums with HEPA filtration systems.
Of course, if you tend to be obsessive, this cycle never ends anyway--so do what pleases you without guilt.
But if you feel the need to do research, here two links: (And for those who need a definitive answer, go with Martha.)
Always start at the top and work
your way down. (gravity)
Dust and vacuum would be wise. Vacuum and dust would be dumb.