The disutility of a pain is a function of the Number of people who experience the pain, the Intensity of the pain, and the Time the pain lasts. It also an increasing function of all three: all else being equal, a pain experienced by more people is worse than one experienced by less people, a more intense pain is worse than a less intense pain, and a longer pain is worse than a shorter one. Or, more formally,
U = f(N,I,T)
âU/âN > 0 (for I,T > 0)
âU/âI > 0 (for N,T > 0)
âU/âT > 0 (for N,I > 0)
[In case that symbol doesn’t display properly, it’s supposed to be a partial derivative sign.]
Furthermore, for all finite N,I,T:
U(0,I,T) = 0
U(N,0,T) = 0
U(N,I,0) = 0
Hmmm… What can we actually agree on?
The disutility of a pain is a function of the Number of people who experience the pain, the Intensity of the pain, and the Time the pain lasts. It also an increasing function of all three: all else being equal, a pain experienced by more people is worse than one experienced by less people, a more intense pain is worse than a less intense pain, and a longer pain is worse than a shorter one. Or, more formally,
U = f(N,I,T)
âU/âN > 0 (for I,T > 0)
âU/âI > 0 (for N,T > 0)
âU/âT > 0 (for N,I > 0)
[In case that symbol doesn’t display properly, it’s supposed to be a partial derivative sign.]
Furthermore, for all finite N,I,T:
U(0,I,T) = 0
U(N,0,T) = 0
U(N,I,0) = 0
Do we at least agree on that much?