Nov 12, 2012
Humans have a value function which is inconsistent over time, discounting roughly with proportion to distance in the future, so that we discount more steeply as an event approaches. This is why we stay up late, ignore the alarm, put off work until close to a deadline, et cetera et cetera.
Yet hyperbolic discounting appears to go away as we mature. I believe this is a result of cognitive mechanisms for maintaining consistency. Cognitive dissonance is painful for us. The consistency mechanism seems to explain some of our irrational behaviour, such as the sunk cost fallacy. It provides a way for us to stick with plans which we previously made, avoiding preference changes due to hyperbolic discounting.
If a hyperbolically discounting agent could perfectly self-modify, it would fix its hyperbola to a specific point in time, resulting in an agent whose discounting would flatten out over the remainder of its life. Perhaps our consistency mechanism approximates this result; but far from perfectly. We can also resolve the inconsistency in a different way, by accepting a specific discount rate. Rather than forcing our future selves to conform to our present preferences, resulting in a gradually flattening function, our present selves may instead accept our future preferences in order to resolve the inconsistency.
Given the difficulty of forcing our future selves to accept a flat distribution, we accept that we will steeply discount in the future as we do in the present. This resolution is popular in some circles; we are often told to "live in the present" or "seize the day". In the extreme case, there is the belief (often associated with mystics) that the present moment is infinitely more important than anything else; the discount factor has collapsed to 0. While this view is intellectually coherent, it seems to be biologically impossible; we will keep taking actions based on future consequences even if we think we are only doing what we desire in the moment. Nonetheless, I suppose we can approach very high discount factors.
Based on this model, my suspicion is that we can approach any discount factor as a self-consistent equilibrium-- it is possible that we learn to make and keep very long-term plans, approximating a very low discount, but it is also possible that we learn to live in the present, or learn anything between these two. The consistency mechanism will want to find a fixed point, but which fixed-point we reach will depend on factors outside these mechanisms.