Could someone please explain any possible justification for exponential discounting in this situation? I asked earlier, but got voted below the threshold. If this is a sign of disagreement, then I would like to understand why there is disagreement.
Robin Hanson’s argument for exponential discounting derives from an exponential interest rate. Our current understanding of physics implies there won’t be an exponential interest rate forever (in fact this is the point of the present article). So Robin Hanson’s argument doesn’t apply at all to the situation in this article, and I strongly suspect Robin Hanson himself would agree that exponential discounting in this situation is ridiculous.
The other reason I see to discount exponentially is exponentially decreasing confidence in our predictions about the future. While this is a good approximation in some cases, its not built into your utility function and arguments like the one in this article don’t make any sense if this is the only basis for exponential discounting.
I have not seen any other arguments in this thread.
Exponential discounting yields time-consistent preferences. Exponential discounting and, more generally, time-consistent preferences are often assumed in rational choice theory, since they imply that all of a decision-maker’s selves will agree with the choices made by each self.
At best, this is an argument not to use non-exponential, translation invariant discounting.
You can discount in a way that depends on time (for example, Robin Hanson would probably recommend discounting by current interest rate, which changes over time; the UDASSA recommends discounting in a way that depends on absolute time) or you can not discount at all. I know of plausible justifications for these approaches to discounting. I know of no such justification for exponential discounting. The wikipedia article does not provide one.
At best, this is an argument not to use non-exponential, translation invariant discounting.
It is an argument not to use non-exponential, discounting.
You can discount in a way that depends on time [...]
Exponential discounting depends on time. It is exponential temporal discounting being discussed. So: values being scaled by ke^-ct—where the t is for “time”.
The prevailing interest rate is normally not much of a factor—since money is only instrumentally valuable.
or you can not discount at all.
That is the trivial kind of exponential discounting, where the exponent is zero.
I know of no such justification for exponential discounting. The wikipedia article does not provide one.
The bit I quoted was a justification. Exponential discounting yields time-consistent preferences. Only exponential discounting does that.
Samuelson did not endorse the DU model as a normative model of intertemporal choice, noting that “any connection between utility as discussed here and any welfare concept is disavowed” (1937, 161). He also made no claims on behalf of its descriptive validity, stressing, “It is completely arbitrary to assume that the individual behaves so as to maximize an integral of the form envisaged in [the DU model]” (1937, 159). Yet despite Samuelson’s manifest reservations, the simplicity and elegance of this formulation was irresistible, and the DU model was rapidly adopted as the framework of choice for analyzing inter-temporal decisions.
The DU model received a scarcely needed further boost to its dominance as the standard model of intertemporal choice when Tjalling C. Koopmans (1960) showed that the model could be derived from a superficially plausible set of axioms. Koopmans, like Samuelson, did not argue that the DU model was psychologically or normatively plausible; his goal was only to show that under some well-specified (though arguably unrealistic) circumstances, individuals were logically compelled to possess positive time preference. Producers of a product, however, cannot dictate how the product will be used, and Koopmans’s central technical message was largely lost while his axiomatization of the DU model helped to cement its popularity and bolster its perceived legitimacy.
I notice that axiomatizations in economics/theory of rationality seem to posses much more persuasive power than they should. (See also vNM’s axiom of independence.) People seem to be really impressed that something is backed up by axioms and forget to check whether those axioms actually make sense for the situation.
Could someone please explain any possible justification for exponential discounting in this situation? I asked earlier, but got voted below the threshold. If this is a sign of disagreement, then I would like to understand why there is disagreement.
Robin Hanson’s argument for exponential discounting derives from an exponential interest rate. Our current understanding of physics implies there won’t be an exponential interest rate forever (in fact this is the point of the present article). So Robin Hanson’s argument doesn’t apply at all to the situation in this article, and I strongly suspect Robin Hanson himself would agree that exponential discounting in this situation is ridiculous.
The other reason I see to discount exponentially is exponentially decreasing confidence in our predictions about the future. While this is a good approximation in some cases, its not built into your utility function and arguments like the one in this article don’t make any sense if this is the only basis for exponential discounting.
I have not seen any other arguments in this thread.
To quote from: http://en.wikipedia.org/wiki/Dynamically_inconsistent
At best, this is an argument not to use non-exponential, translation invariant discounting.
You can discount in a way that depends on time (for example, Robin Hanson would probably recommend discounting by current interest rate, which changes over time; the UDASSA recommends discounting in a way that depends on absolute time) or you can not discount at all. I know of plausible justifications for these approaches to discounting. I know of no such justification for exponential discounting. The wikipedia article does not provide one.
It is an argument not to use non-exponential, discounting.
Exponential discounting depends on time. It is exponential temporal discounting being discussed. So: values being scaled by ke^-ct—where the t is for “time”.
The prevailing interest rate is normally not much of a factor—since money is only instrumentally valuable.
That is the trivial kind of exponential discounting, where the exponent is zero.
The bit I quoted was a justification. Exponential discounting yields time-consistent preferences. Only exponential discounting does that.
Not sure why your earlier comment got voted down. I voted it up to −1.
I think exponential discounting has gotten ingrained in our thinking mostly for historical reasons. Quoting from the book Time and Decision: economic and psychological perspectives on intertemporal choice (“DU model” here being the 1937 model from Paul Samuelson that first suggested exponential discounting):
I notice that axiomatizations in economics/theory of rationality seem to posses much more persuasive power than they should. (See also vNM’s axiom of independence.) People seem to be really impressed that something is backed up by axioms and forget to check whether those axioms actually make sense for the situation.