Tuesday, June 7, 2011

Parables of misunderstood causality

I. Basketball players are taller than average. Personal trainer observes this and starts a "get taller" program which promises to add inches of height by having the trainees play basketball intensively.

We all know what is wrong with the trainer's idea: basketball players don't get tall because they play basketball, they play basketball because they are tall. (And a lot of other things too, but this is the direction of the implication.)

About 90% of fitness programs (let alone other, more important things) are less obvious, but equally wrong, forms of this parable. (Technically, thinking that $a\Rightarrow b$ is $b \Rightarrow a$.)

II. Students who listen to their lectures as podcasts while exercising perform better than those who don't. School administrator observes this, buys every student an iPod (with the student's money); expects increase in performance.

The problem with the administrator's idea is that the students who had chosen to listen to the lectures as podcasts are probably the students who apply themselves to their studies in other ways, say by paying attention in class and doing their homework assignments diligently; in other words, the students who are using the podcasts as complements to the lectures. Because their dedication to the schoolwork is what drives their school results, giving the other students iPods is unlikely to change their performance.

This is a common problem with from-the-top intervention in individual decisions: observe a behavior that is causing some advantage to a segment, and impose that behavior on others without taking into account the effect of self-selection of the segment to begin with. (Technically, thinking that $(a \Rightarrow b) \wedge (a \Rightarrow c)$ is $b \Rightarrow c$.)

III. Science fiction audiences are more loyal to their entertainment products and more likely to buy complementary products than the average audience. Executive in charge of a science fiction channel wants to increase the reach of the programs in order to get this same profitable behavior from a larger audience, and adds elements that appeal to general audience to the channel's programming.

Not only is the sci-fi channel now competing with other channels which are better at targeting the general audiences and therefore fails to capture any significant part of the general audience, but the sci-fi audience is likely to seek more targeted entertainment, moving away from the sci-fi channel. In addition, any members of the general audience that happen to watch sci-fi programs are not going to display the same loyalty as the original audience (because they only have a passing interest in the sci-fi part of the programming) and the members of the sci-fi audience are likely to become less loyal and buy fewer complementary products (because the in-group signaling value of these products is diluted by the attempted broader audience reach).

This is called the law of unintended consequences, though sometimes one wonders if the people making these decisions don't actually intend the consequences and just lie about their original intent. (Technically, thinking that $(a \wedge \neg b \Rightarrow c) \wedge (a \wedge b \Rightarrow \neg c)$ is $a \Rightarrow c$.)

Edited at dinnertime to add a fourth vignette:

IV. Baddoofus is the tyrant of Toortonia; there's a rebellion that he is putting down brutally. Goodniknia, a military superpower, takes pity on the rebels and negotiates a peaceful change of power, including immunity for Baddoofus. Two months later, the former rebels, now in power, arrest and execute Baddoofus, without any repercussions from Goodniknia. A little later, in nearby Pomponia, tyrant Foolmenot starts having problems with his rebels and repressing them brutally; Goodniknia expects its negotiators to help bring a peaceful resolution to the Pomponia crisis as well.

Rationally Foolmenot should fight to death, for death is what Baddoofus case shows will happen to any former tyrant who accepts the Goodniknian agreements, expecting them to be respected by the rebels or enforced by Goodniknia. No matter how much force Goodniknia brings to bear, a possibility of death is a better choice than a certainty of death.

The misunderstood causality in this case is called one-step lookahead myopia, that is, Goodniknia chooses to let the Toortonian rebels execute Baddoofus since he was a bad guy, ignoring the effect of that decision on the decisions of future tyrants. (Since this example requires either modal logic or a probabilistic framework, I'm not going to formalize it.)

One-step lookahead myopia is a very common decision trap, both for managers and for policy makers, especially when combined with the other three causality misattributions. A common managerial example of one-step lookahead myopia is the use of ratcheting incentives: by changing demands or budgets depending on previous performance or costs, companies create incentives for their employees to game the ratcheting, for instance by making sure that they never over-perform (which would raise expectations).*

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* In an episode of The Rules Of Engagement, married Jeff tells engaged Adam to give his fiancée a bad birthday present so that Adam never has to come up with good presents after he gets married. This is an example of the problem with ratcheting incentives and consequently with one-step lookahead myopia on the fiancée's part.