I'm thinking [u]analog multiplexer[/u] chips. But, you'd need inputs & outputs (for the positional feedback) and it might get tricky if you need to move more than one fader at a time.
FYI - The Arduino ATmega chip has multiple analog input pins, but internally there is only one (multiplexed) analog-to-digital converter. Under "normal conditions" it runs fast enough that it appears to be reading the inputs simultaneously.