Authors: Gerd Gigerenzer and Daniel G. Goldstein
Source: Psychological Review 1996, Vol 103. No 4 650-669
Link: PDF

The central tenet of this paper is that rationality in human decision making (Homo Economicus), isn’t a realistic assumption, despite the niceties it provides for model creators. It Notes that historically there have been 3 school of thought on human decision making:

1. Classical thinkers such as Pierre, Laplace or Piaget asserted that humans make decisions based solely on the use of probability ans statistics. In fast “the Enlightenment probabilists derived the laws of probability from what they believed to be the laws of human reasoning”. Despite much of science moving on past this, Economics and Psychology have held on to this view for the most part
2. In the mid-late 20th century, the “heuristics and biases” movement, pioneered by the likes of Tversky and Kahneman concluded that “human inference is systematically biased and error prone.” Despite the seeming repudiation of the 1st school of thought, this school holds on to probability and statistics as the normative way to make decisions, we humans are just in actuality broken or not up to the task.
3. The authors subscribe to Herbert Simon’s notion of bounded rationality, characterized by both cognitive and ecological bounds. The cognitive bound is simply that humans do not have the mental tools to quickly do the complex calculations necessary to perform multiple regression. Secondly, the ecological bound states the the human mind has adapted to live in real world environments.

The authors have taken these Simon’s two assertions and go on to propose a number of satisficing algorithms, that:

“operate with simple psychological principles that satisfy the constraints of limited time, knowledge, and computational might, rather than those of classical rationality”

For the experiment to test their algorithms, they take on a two alternative choice task where the subject is forced to make an inference based on knowledge that the user already has. Forcing them to retrieve this from memory presumable simulates the ecological bound. The theories that they propose build on Gigerenzer’s previous work on Probabilistic Mental Models (PMM). The theory integrates 3 central ideas:

1. “inductive inference needs to be studied with respect to natural environments” (Brunswik & Simon)
2. “inductive inference is carried out by satisficing algorithms” (Simon)
3. “inductive inferences are based on frequencies of events in a reference class” (Reichenbach)

Ultimately, the algorithms that conform to the PMM tenets don’t perform exhaustive memory search nor do they perform complex interactions between data points. Gained by not performing these expensive operations is very fast decision making. The authors assert that this is very valuable when being chased by a tiger, or say deciding whether or not to exit the freeway. Always getting off at the correct exit is less important than always deciding quickly enough that you don’t crash. Not taking into account all information conveniently allows for easily modeling of incomplete information instances, which are presumably the vast majority of real world decision making cases.

In their experiment they assess the capacity of a subject to guess whether city a has a greater population than that of city b. They do this for a set of cities known, this set is the reference class. The subject has certain data about each city, such as whether it has a soccer team or a university. These data points are known as cues. They model limited knowledge (incomplete information) as both an imperfect knowledge of all objects in the reference class and limited knowledge of the cue values (facts about the cities).

The authors finally propose a very simple satisficing algorithm called the “Take the Best Algorithm“. This algorithm assumes a subjective rank order of cues according to their validities. It has 5 steps:

1. Recognition Principle: This is invoked when recognizing an object is a predictor of the target variable. In the case of population, there is an obvious correlation. Thus, if we are predicting highest population size and one of the two cities is know, pick it. If neither are known, randomize. If both are known go to step 2.
2. Search For Cue Values
3. Discrimination Rule: Decide if the cue discriminates.
4. Cue-Substitution Principle: If so use it to pick, otherwise pick another cue (step 2)
5. Maximizing Rule For Choice: Choose the value the cue would predict. If they are the same randomize.

This algorithm searches only a portion of the total knowledge, that is it reads only a subset of the cues for either object. It also does not attempt to integrate information, but rather just substitute in the best cue.

The authors then assert that experimental evidence has shown that the less is more effect can be shown to exist empirically when one uses this algorithm. This may explain why US students make slightly more correct inferences about German cities and vice versa.

Note that one may not know a cue value for all objects in the reference class. Thus, the authors define two properties that they use to evaluate cues. Ecological Validity is the proportion of cases in the reference class in which this cue is an accurate predictor (not a bad prediction). Discrimination rates are the relative frequency with which the cue can be used to discriminate (not the same value).

They then present data comparing the Take the Best (TTB) algorithm wit h the following other algorithms:

1. Tallying
2. WeightedTallying
3. Unit-Weight Linear Model
4. Weighter Linear Model
5. Multiple Regression

Ultimately they conclude what you would predict. The TTB algorithm is the fastest due to the small number of comparisons needed. They also assert that it does just as well if not better than all of the other algorithms. While their data does seem to bear this out with 84 German cities and 6 cues, even with perturbation of the amount of known data (they randomize over which objects are recognized and which cue values are known), their methodology for cue selection isn’t explained in much detail. I will be curious to see if there is follow up work that tries to see if these results were come by due to a fortuitous selection of cues and objects int he reference class.

At the end the suggest two simpler algorithms, the “Take the Last” algorithm and the “Minimalist” algorithm that require even fewer cue comparisons (calculations) and do only marginally worse then the TTB algorithm.

They conclude the paper by addressing “One Reason Decision Making”, that is the decision is made based on one good reason and there is no compensation between cues. This is the case often when using the TTB algorithm. They note that the recognition principle is an example of one reason decision making that exploits lack of knowledge. They suggest as support for why one reason decision making may be plausible and good is that much evidence supports the notion that humans are ill equipped to deal with correlation between cues.

In summary the authors suggest that despite the cleanliness of many of the normative models that are so prevalent in much of academia, cognitive models based on normative assumptions are unrealistic and possibly unnecessary. The brain is constrained in the complexity of calculations it can perform, the speed with which it can perform them, and the data upon which it can draw to make those calculations. Thus, any realistic cognitive algorithm would take that into account. They propose that the TTB algorithm is a reasonable attempt at an algorithm that meets all of those criteria.