If “at the same time” is meant to modify “the same goods”, so that what you’re saying is that discounting does not involve assigning different values to “good-g-at-time-t”, then this is false. Depending on the time at which the valuation is made, discounting entails that different values will be assigned to “good-g-at-time-t”.
Suppose an agend with exponential time discounting assigns goods G at a time T a utility of U0(G)*exp(a*(T0-T)). Then that is the utility the agent at any time assigns those goods at that time. You may be thinking that the agent at time TA assigns a utility to the goods G at the same time T of U0(G)*exp(a*(TA-T)) and thus the agent at different times is assigning different utilities, but these utility functions differ only by the constant (over states of the universe) factor exp(a*(TA-T0)), which being an affine transformation, doesn’t matter. The discounting agent’s equivalency class of utility functions representing its values really is constant over the agent’s subjective time.
Suppose an agend with exponential time discounting assigns goods G at a time T a utility of U0(G)*exp(a*(T0-T)). Then that is the utility the agent at any time assigns those goods at that time. You may be thinking that the agent at time TA assigns a utility to the goods G at the same time T of U0(G)*exp(a*(TA-T)) and thus the agent at different times is assigning different utilities, but these utility functions differ only by the constant (over states of the universe) factor exp(a*(TA-T0)), which being an affine transformation, doesn’t matter. The discounting agent’s equivalency class of utility functions representing its values really is constant over the agent’s subjective time.
Ah, I see. You’re right. Comment retracted.