Abundant Information
A theorem shows that Dawes’ Rule makes perfect inferences in a finite environment containing every possible uncertain but favorable binary cue. This idealized result explains one way abundant information can favor a linear model; ordinary collections of many cues need not meet its conditions.
THE IDEA
Abundant Information
Adding cues to a scarce environment will do little for Take the Best if the best cues in the original environment are already highly valid, but it may compensate for various mistakes Dawes’ Rule would have made based on the first cues. In fact, by adding and adding cues we can make Dawes’ Rule achieve perfection. This is true even if all cues are favorable (i.e., their validity is *>*0.5) but uncertain (i.e., their validity is *<*1).
THEOREM Assume that the environment consists of N ≥ 5 objects. If an environment consists of all possible uncertain but favorable cues, Dawes’ Rule will discriminate among all objects and make only correct inferences.
The proof is given in Martignon et al. (1997). Note that we are using the term cue to denote a binary-valued function on the reference class. Therefore, the number of different cues on a finite reference class is finite. The theorem can be generalized to linear models that use cue validities as weights rather than unit weights. Under these abundant-information conditions, linear models can outperform Take the Best on average.
When to use it
Stock market analysis: combining dozens of financial ratios to predict stock performance.
College admissions: using multiple criteria (GPA, test scores, essays, extracurriculars) to rank applicants.
Customer churn prediction: aggregating many behavioral signals to identify likely churners.
Quality control: using many inspection checks (each slightly indicative) to classify products as defective or not.
FROM THEORY TO EVERYDAY LIFE
In practice
Hiring Decisions with Multiple Interview Questions
Suppose binary hiring cues each have validity above 0.5 but below 1. That alone does not meet the theorem’s requirement that every possible uncertain, favorable cue be available. Adding questions may help Dawes’ Rule, but it does not guarantee a perfect ranking. Take the Best checks cues in order and stops at the first one that distinguishes the candidates.
Medical Diagnosis from Multiple Symptoms
Suppose symptoms have predictive validity around 0.6. Combining many of them does not automatically reproduce the theorem’s complete cue environment or guarantee correct diagnoses for all patients. Their overlap and predictive value need to be assessed on data.
A MOMENT TO REFLECT
Put it to work.
In a decision with many cues, when might adding more cues actually reduce accuracy instead of improving it?
How does the concept of 'abundant information' challenge the notion that simple heuristics are always superior?
Can you think of a situation where you instinctively used a 'take the best' approach but later realized a more comprehensive model would have been better?
Often confused with
References
- Martignon et al. (1997) — Martignon, L., et al. (1997)
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)