If Dogs Know Calculus, Does It Follow That Addiction Is the Optimal Solution to an Intertemporal Choice Problem under Perfect Information?

In the comments to my post containing Ole Rogeberg's video on the Becker-Murphy theory of rational addiction, Ant Manelope writes:
My dog does calculus and geometry. When I throw a stick across a river diagonally, he doesn't swim straight for it, nor does he swim perpendicular to the river, but at some angle in between which approximately minimizes his effort.
And TGGP adds:
A better calculus example would be catching a ball in mid-air, which involves acceleration problems difficult to solve in real-time with a calculator.
Yes, dogs sometimes behave as though they knew calculus, and bumblebees leave an optimal amount of nectar behind in flowers. The oomph of these examples is somewhat reduced by the fact that stupid behaviour by animals would hardly be seen as a devastating strike to the homo oeconomicus model. But they certainly do show that there can be behaviour that proceeds as if the agent had done complex mathematical calculations when s/he clearly hasn't.

We can expect to see this kind of behaviour to the extent that the problems we are looking at were stable, recurring and important during the time in which the agents in question evolved. With such problems (e.g., the laws of physics), evolution has had ample time to approach the optimal solution by means of selection. In contrast, we should expect to be ill-equipped to deal with evolutionary novel stimuli, such as heroin - unless we're simply lucky. Indeed, it is a standard interpretation to see addiction as the reward system's response to stimuli for which it wasn't built. Owen Jones calls this kind of phenomenon "time-shifted rationality".

None of which, of course, has to do with the silly perfect information assumption.


Doc Merlin said...

The perfect information assumption isn't silly, its there to make the model simpler to better understand the process. You can always add in uncertainty later. Also, also the homoskedastic portions of the uncertainty will vanish as your sample size of individuals increases.

LemmusLemmus said...

You can simplify a model so that it becomes silly - no contradiction there. Not sure how to interpret the bit about homoskedasticity, which I only know as a technical term in regression analysis.

Human Mathematics said...

Excellent point about evolution. Can you elaborate more on the perfect information assumption? You're saying that the authors assume that we know exactly what will happen in the future?

With respect to heroin addiction that's not necessarily silly. I mean, we've all seen movies about addicts, and heroin users usually know other heroin users, some who have overdosed.

LemmusLemmus said...


you can find the full original article <a href="http://www.drugtext.org/library/articles/becker02.htm>here</a>. The perfect information assumption goes well beyond knowing that heroin can be harmful, it involves knowledge about the effect of concurrent consumption on all future states. Illustrative quotes from the link above:

"Some critics claim that the model in Stigler and Becker (1977)presumably also the model in this paper-is unsatisfactory because it implies that addicts are "happy," whereas real-life addicts are often discontented and depressed (see, e.g., Winston 1980). Although our model does assume that addicts are rational and maximize utility, they would not be happy if their addiction results from anxiety-raising events, such as a death or divorce, that lower their utility. Therefore, our model recognizes that people often become addicted precisely because they are unhappy. However, they would be even more unhappy if they were prevented from consuming the addictive goods."

"In our analysis, binges do not reflect inconsistent behavior that results from the struggle among different personalities for control. Rather, they are the outcome of consistent maximization over time that recognizes the effects of increased current eating on both future weight and the desire to eat more in the future."