Chemistry - Pressure Cooker at High Altitudes and Low Altitudes
Edit - As 1e9dB's answer points out I made a huge mistake in this answer. The inside pressure of the pressure cooker is ambient pressure plus the extra pressure of the valve. The pressure cooker does not cook at an absolute pressure independent of altitude.
You have it all backwards. The pressure cooker allows the pressure inside the cooker to be above the sea-level atmospheric pressure which also increases temperature inside the cooker and thus decreases cooking time. So the critical factor is the increase of the boiling temperature of water as a function of the pressure inside the cooker.
The pressure cooker raises the pressure inside the cooker to the same absolute pressure, regardless of the altitude at which the cooking is being done. A typical value for the internal pressure would be about 2 atmospheres absolute which makes the internal cooking temperature about 120 °C. (The steam is pushing against the pressure regulator (weight) to escape, not the outside atmosphere. It is like the safety valve on an old steam locomotive that keeps the pressure at a certain level so that the pot doesn't blow up.)
The inside temperature of a pressure cooker when steaming (120 °C) is way below the critical temperature of water (about 374 °C) so that factor doesn't enter into the cooking time at all.
MaxW has it right except for one thing - the pressure inside the cooker does in fact does depend on altitude. For example, a cooker that will reach 15 psi at sea level will only reach about 12.5 psi in Denver.
Although it is true that the pressure is regulated by a weight which closes off a small hole, and the weight is constant regardless of altitude, remember that the ambient pressure outside the cooker is also imparting a downward force on the weight that is in opposition to the internal pressure that is imparting an upward force. At a higher altitude the internal pressure can't rise quite as much before it overcomes the lower external pressure in order to raise the weight. The result is that the internal pressure is lower by exactly the same amount as the ambient pressure difference due to altitude. That means that the boiling point inside the cooker is somewhat lower at higher altitude, although still higher than it would be outside of a pressure cooker.
Thus at higher altitude you need to increase the cooking time: Pressure Cooker PSI FAQ