To the best of my knowledge, a wastegate works as follows.
Both atmospheric pressure and spring force holds the valve closed and boost pressure acts on the other side to blow it open. Exhaust pressure difference will also act against the valve face, but the valve is normally a lot smaller than the diaphragm.
The boost pressure will be maintained at ambient atmospheric which is variable, plus the spring which is constant while the valve is on the seat, unless deliberately reset, so due to this, a turbo engine will normally drop of power at reduced atmospheric density, but it will not fall off by as much as an NA engine will, so it is partly but not fully compensating.
The magnitude of the partial self correcting will be proportional to the ratio of atmospheric pressure to spring pressure.
There will also be a small variation due to exhaust pressure on the valve, but it should be much smaller than the other forces involved, and will tend to increase with speed and with increased air density as that will produce more exhaust gas. That will tend to further diminish the self regulating tendency.
To further complicate it, the increased exhaust gas will require the waste gate to open further, thus increasing effective spring pressure and so offsetting to some degree the effect of exhaust gas pressure on the valve.
Regards
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