Discounting of future goods does not involve assigning different values to the same goods at the same time.
The qualifier “at the same time” is ambiguous here.
If you mean that different values are assigned at the same time, so that the agent has conflicting utilities for a goal at a single time, then you’re right that discounting does not involve this. But neither does Future Tuesday Indifference,. so I don’t see the relevance.
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”.
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.
The qualifier “at the same time” is ambiguous here.
If you mean that different values are assigned at the same time, so that the agent has conflicting utilities for a goal at a single time, then you’re right that discounting does not involve this. But neither does Future Tuesday Indifference,. so I don’t see the relevance.
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.
Ah, I see. You’re right. Comment retracted.