On January 6, 1995, a man walked into two banks in Pittsburgh and tried to rob them both. He wore no mask. The surveillance cameras caught him with a gun, standing in front of a teller.
His picture ran in the Crime Stoppers segment of the eleven o’clock news. Less than an hour after the broadcast, police arrested McArthur Wheeler, 45. He could not believe it. “But I wore the juice,” he said.
He had rubbed lemon juice on his face, believing it would make him invisible to video cameras. It burned his eyes, so he squinted. He had tested the theory first, detectives told the Pittsburgh Post-Gazette. He took a Polaroid of himself, and his face wasn’t in the picture.
A sergeant’s guesses included bad film and a camera pointed the wrong way. Wheeler ran a check, the check said yes, and he walked into two banks.
Bottom quarter, 62nd percentile
David Dunning, a psychologist at Cornell, found the story in the 1996 World Almanac, among the offbeat news. As Errol Morris later told it in The New York Times, a thought followed: if Wheeler was too stupid to be a bank robber, perhaps he was also too stupid to know it.
Dunning and his graduate student Justin Kruger set out to measure it. In four studies, published in 1999, they tested college students on humor, grammar and logic, then asked how well they thought they had done. Those who scored in the bottom quarter had landed around the 12th percentile. They put themselves in the 62nd.
The authors’ explanation was a dual burden. People who lack a skill, the paper argued, “reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the metacognitive ability to realize it.”
On that reading, the bottom scorers were like a proofreader who can’t spell: the page looks clean to him, because the skill that would flag the errors is the one he lacks. The authors reported support for it. When they improved some participants’ skills, those participants got better at recognizing the limits of their ability.
People with less skill tend to overrate themselves; why is still argued over.
Then statisticians took a closer look at the 1999 graph.
A chart that random numbers can draw
In 2016 Edward Nuhfer and colleagues used random-number simulations to argue that the usual way of charting self-assessment data, groups sorted by score, can “introduce artifacts that invite misinterpretation.” The psychologist Patrick McKnight later fed a computer purely random test scores and self-estimates and drew the chart. The lines, as Jonathan Jarry wrote for McGill University’s Office for Science and Society, looked “eerily similar” to the original.
Sort people by real score, and if their guesses are noisy, the bottom group’s average guess will sit above its score and the top group’s below. Add the common habit of rating yourself above average, and the bottom gap grows. Nobody has to be blind for the picture to appear.
In 2020 Gilles Gignac and Marcin Zajenkowski used methods built to sidestep this trap, testing 929 adults on reasoning and asking them to rate their own intelligence. The link between real and self-rated intelligence came out “essentially entirely linear.” The effect, they concluded, “may be much smaller than reported previously.”
Dunning’s team had answered earlier critics in 2008, reporting that poor performers still lacked insight in real-world settings and when given incentives to be accurate. The argument is not settled.
What holds either way: the bottom group did, on average, place itself around the 62nd percentile. What is disputed is why: whether lacking the skill is what hides it, or whether everyone’s self-estimates are this fuzzy and the bottom group simply has the most room to be wrong upward. “The effect is about us, not them,” Dunning wrote to Jarry.
The forecast that looked fine
Say you came up through sales and have just taken over a team of analysts. One of them sends you next quarter’s forecast. The chart is clean and the totals add up. You feel sure it’s fine.
Whichever side is right, that feeling tells you little here. On the original reading, spotting a broken forecast takes the analyst’s skill, which you were never hired for. On the critics’ reading, your self-estimate is as noisy as anyone’s, and in forecasting you sit near the bottom, with the most room to be wrong upward.
What you can check has an answer key: last year’s forecasts from the same model set against what actually happened, or a second analyst who reads the assumptions before you sign. A check you design and grade yourself leans on the very judgment in question.
The model that knew what it knew
A language model has a confidence of sorts. Before it picks A, B, C or D, it gives each option a probability. In its 2023 technical report, OpenAI scored those numbers for GPT-4 on part of the MMLU benchmark. The pre-trained model, before the extra training that shapes it into an assistant, was “highly calibrated”: its confidence generally matched how often it was right. Post-training, in the words of the report’s chart caption, “hurts calibration significantly.”
What carries over is the answer key: the only way to see the gap between confidence and correctness is to score one against the other.
What differs is where the gap came from. OpenAI reports that the base and post-trained models did about equally well, on average, on the multiple-choice exams it tested. By that measure, the confidence drifted while the skill held. That looks less like the 1999 story than like the critics’ picture, with confidence and skill moving apart for reasons of their own.
Wheeler’s proof was a Polaroid he may have pointed the wrong way. A model can be scored against thousands of questions with known answers.