I want to know if a washer that does 2 gpm @ 2000 psi has only half the
"cleaning power" as one that can do 4 gpm at 4000 psi (ie does the
cleaning power scale linearly with these numbers, or geometrically or
exponentially).

Another way of looking at these two washers is to make a more
common electrical comparison. This comparison difference will hold
true in pressure washers also.

2gpm @2000 psi would be represented by 2amps @2000 volts

4gpm @4000 psi would be represented by 4 amps @4000 volts

Power = Voltage x Amperage So........
The 2gpm washer equals 4000 units of cleaning power
The 4gpm washer equals 16000 units of cleaning power

* units of cleaning power undefined
* units of cleaning power are for reference/comparison only