The basic responses are correct that the eye's perception is non - linear, and sensitive to the color temperature, wavelength mixture, etc.
On the positive side, your eye does not need to double the brightness in order to see better, and you can enhance the effective result by thinking through how your eye works with various light sources and color mixtures.
In Paul's case, you see a dramatic example of how not only brightness, but color content is affecting vision. Part of his challenge is not just the overall brightness, but the color content. He is using a white light which contains some RED / Orange to shine through an orange cone. Most of the light is absorbed by the cone (like a filter) and the R/O part shines through. If he uses a different lamp with a different color temperature distribution for the illumination, the R/ O content can change dramatically, even for similar power, and perhaps even the same Lumen rating.
As an alternative, if he used a lamp which had an output entirely in the Red / Orange region, the overal Lumens rating and power ratings might be substantially lower, but the absorbtion losses due to the cones filtering would be very low. In this case, if he used Lux III R / O, (not sure how many with out calculating it, but maybe even 1), his visibility would improve and power draw would be well under 5 watts, maybe even 1/2 of that.
This example (applied to traffic lights) is the exact reason why LEDs became known for being more efficient than incan bulbs. For monochromatic applications, they are hard to beat, for white - its a more complex answer.