Professor Gilbert’s Illusion

Intuition is not like vision. Really.

Posted Jan 05, 2017

J,. Krueger
Screenshot from Dan Gilbert's bad decisions TED talk
Source: J,. Krueger

Just in case you’re not getting it. ~ Dan Gilbert, youtube professor, driving a point home

Years ago – in 2008 – Dan Gilbert gave a TED talk on “Why we make bad decisions” (transcript here) The talk was rated “fascinating” and “informative” on the TED site and it is worth watching – in part for reasons not intended by Dan. What, in fact, did Dan intend? Perhaps he intended to tell us that all our decisions are bad, that most are bad, or that the ones that matter the most are bad. We do not know. We do know, however, that Dan is of the school of thought that regards psychological errors as the most important phenomena a psychologist can find and show to the public. This is a heavy prejudice to bring to the study of mind, and it leads to surprising and awkward moments, as we shall see momentarily.

Dan starts by introducing Daniel Bernoulli’s insight that choice in an uncertain world can be modeled as a choice between the expected values of available options. Each option has a value or price, and each option is realized with a particular probability. Multiply the value with its probability, so Bernoulli, and choose that option with the higher expected value. The implication of this decision rule is that choice is trivial when values and probabilities are well known. Dan the Younger notes – correctly – that values and probabilities are often not well known and that people have to estimate them. He also notes – again correctly – that estimates can be quite poor (although he puts it hyperbolically as “people are horrible at estimating both these things”), thereby leading to poor decisions.

Dan then gives some vivid examples of estimation errors. For probability estimates his shrift is short. He relies on stock examples of the availability heuristic – perhaps these came to mind most easily. For instance, people think it more likely to die by homicide than drowning, mainly because cases of the former receive more news coverage.  

Dan’s main mission is to reveal our unconfessed inability to estimate value correctly and reliably. He asks whether we would spend $25 on a hamburger, predicts that we would say no, and asserts that we did not consider all opportunity costs under all circumstances. We would, Dan reveals, gladly pay $25 for a burger on a long-distance flight without food service. The original question was thus unfair because its answer was underdetermined and the opportunity costs (what else we could do with the money) too many to contemplate. We did not know of Dan’s extravagant context of meal-less aviation, which eliminates all opportunity costs. A fairer question is “Would you pay this amount for this product under current circumstances?” And then our answers might not be so bad.

Next, Dan sides with the economists, whom he otherwise disdains (“I think there's many good reasons not to listen to economists,” he offers in post-talk discussion), in asserting that what matters is total wealth, not changes in wealth. People abhor declining income even when its sum total is greater than the total income obtained from constant or even rising pay. This example gets him to the topic of bad comparisons. “One of the things we know about comparisons: that when we compare one thing to the other, it changes its value.” Comparisons with the past can be problematic if they invite sunk cost effects, and so can be comparisons with irrelevant standards or foils. Dan has us imagine a $33 bottle of wine, which is either the most expensive bottle on the shelf, or placed between a $20 bottle and a $50 bottle. In the latter case, the $33 bottle looks like the reasonable choice, allowing us to enjoy a drink at moderate expense. When people know little about how to assess and scale value, context is valuable, even if this means that context can be strategically exploited. “Shifting comparisons can bedevil our attempts to make rational decisions,” Dan concludes, and the little word can is critical here. Dan does not ask what we should do instead, if or how we should get rid of shifting comparisons, or comparisons altogether. He seems to imply that we should be expert oenophiles who infallibly appraise a vintage’s absolute value. I find this suggestion unreasonable.

Pressing on, Dan laments that we’d be happy to drive across town to save $100 on a $200 purchase but not to save the same amount on a $30,000 purchase (a shifting comparison). Dan the Younger follows Dan the Èlder (Bernoulli) and his quest for expected value. But actually, Bernoulli (173/19548) realized that fixed amounts are psychologically worth less if they are part of a greater bundle of wealth, a realization that took him from value to utility, and fame.

Then we get to the punch line: comparisons that shift over time and thereby introduce choice reversals. Such reversals are well-documented in the literature on intertemporal choice. In Dan’s example, we prefer $50 now over 60$ in a month, but also prefer $60 13 months from now over $50 12 months from now. Money loses real and perceived value over time. Economists (e.g., Samuelson, 1937) assume that the discount rate is geometric (i.e., exponential). With the passage of each fixed period of time, a good loses a certain fixed percentage of its value. If this were so psychologically, there would be no choice reversal when the two options, the sooner and the later, are both moved into the future by the same extent. I have commented elsewhere that the incoherence of preference reversals conventionally receives surplus meaning such that the closer preference (impatience) is considered bad, while the remoter (prudence) one is considered good. My point was that this conclusion cannot rationally be drawn from the mere existence of intertemporal incoherence, and that it may be patience shown in postponed choice that is ill-advised.  

Dan chooses an intriguing gambit to illustrate intertemporal choice reversals, and this is where things go wrong. Go to minute 20 in the TED talk and look at the displays of the fireman and the fiddler. The fireman is taller than the fiddler, and this remains so when both recede into the distance. We know that they are receding and not just shrinking from the sparse depth cues suggesting a third dimension. This is critical, but Dan doesn’t mention it. He makes some of the stick figures disappear, only showing the fiddler at distance X and the fireman at distance X + 1 foot. The astonishing result is that “at a very close distance, the fiddler looks taller than the fireman, but at a far distance, their true relations are preserved.” There the fireman looks taller than the fiddler, although the fireman is 1 ft farther away. Notice the claim that at a far distance the perceived difference in height reflects the true difference, although the fireman is farther away. This suggests the inference that perception at a short distance, where the fireman looks smaller, is the problem.

Dan’s argues by analogy. He claims to show a visual illusion whereby we see true relations only at a great distance, but get things wrong when they are right in front of us. At a close distance, the fireman’s perceived shrinkage, leaving him to look smaller than the fiddler although he the fireman is only one foot farther away, is the visual mistake we make. By analogy, it is a cognitive illusion to devalue $60 dollars so that they feel they are worth less in a month than $50 today. The analogy is legit, so Dan, because Plato said that “what space is to size, time is to value” [I have been unable to verify this quote; my search turned up only references to Gilbert attributing this to Plato].

But is the analogy legit? Dan’s fireman-fiddler illustration shows quasi-hyperbolic shrinkage over distance. As a foot of distance is added, there is a great loss of perceived size at first, and then less and less of a proportional loss as more distance is added. Dan constructed the demonstration to make it so and to thereby devise a visual analogy of value discounting over time. The problem is, as best as I can tell after asking several vision scientists, that the reduction of perceived object size over distance is geometrical rather than hyperbolic, which means it does not yield the kind of size inversion claimed by Dan. Dan, it would seem, invented a visual illusion to legitimate the claim – by analogy – that preference reversals of value over time are also illusory. I asked Dan if he could direct me to the research that demonstrates hyperbolic discounting of size over distance. He could not. This certainly does not prove that no such discounting can occur, but the onus of proof is Dan’s.

Why bother? We should bother because the idea that visual illusions are prototypes of judgment and decision illusions has become a trope, an article of faith, a cliché. Tversky & Kahneman (1974) once suggested this analogy, and since, Kahneman (see this post), Ariely (see this post) as well as Gilbert and friends have gone wild with it. Some of us think this analogy is as false as it is facile (Felin, Koenderink & Krueger, 2016). It is time to re-assess, rationally, if we may.

Bernoulli, D. (1738/1954). Exposition of a new theory of the measurement of risk. Econometrica, 22, 22-36. Translated by L. Sommer.  

Felin, T., Koenderink, J., & Krueger, J. I. (2016). Rationality, perception, and the all-seeing eye. Psychonomic Bulletin & Review. Online first, December 7. DOI 10.3758/s13423-016-1198-z

Samuelson, P. (1937). A note on measurement of utility. The Review of Economic Studies, 4, 155-161.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases, Science, 185, 1124-1131.