The Asylum Judges Who Couldn't Say Yes Twice

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Picture a US immigration judge on an ordinary morning. The docket is full. One after another, asylum seekers come before the bench, each with a different country, a different story and a different amount of evidence that going home would put them in danger. The judge hears the first case and grants asylum. Then the next case begins. Nothing about the second applicant has anything to do with the first. They didn't arrive together, they don't know each other, and their claims rise or fall on their own facts. So the first decision should tell you precisely nothing about the second.

It does, though. When the economists Daniel Chen, Tobias Moskowitz and Kelly Shue went through 150,357 US asylum decisions made between 1985 and 2013, they found that judges were up to 3.3 percentage points less likely to grant asylum if they had approved the previous case than if they had denied it. After two grants in a row, the chance of a third fell further. The same pattern turned up in two completely different jobs: Major League Baseball umpires were 1.5 percentage points less likely to call a pitch a strike if they had called the previous pitch a strike, and loan officers reviewing files in a field experiment in India showed it too. Published in the Quarterly Journal of Economics in 2016, the paper's title named the culprit: the gambler's fallacy.

The mechanism: chance doesn't keep score

The gambler's fallacy is the belief that independent random events balance themselves out over short stretches. Red has come up five times, so black is due. A coin has landed heads three times, so tails is overdue. It isn't. The wheel and the coin have no memory, and each spin or toss starts from scratch.

The deeper error is a wrong picture of what randomness looks like. Ask people to write down a “random” sequence of coin tosses and they alternate too much and avoid long runs, because streaks feel like a pattern. Real randomness is streakier than intuition expects: in a run of 20 fair coin tosses, a streak of four or more of the same face is more likely than not. Psychologists call this the belief in the law of small numbers: expecting a short sequence to look like the long-run average.

Now put that belief in a decision-maker. A judge who has just granted two cases starts to feel that a third grant would be one too many, as if a fair docket should come out roughly balanced within a morning. Nobody decides to ration approvals. It just starts to feel wrong to say yes again, and so the next applicant, whose case has nothing to do with the last two, gets a slightly harder look. That's the sense in which the decisions become negatively autocorrelated: each one leans against the one before it, for reasons unrelated to the merits.

The researchers found the effect was strongest exactly where you'd expect it: among less experienced and more moderate decision-makers, after longer streaks, when consecutive cases were close together in time or looked similar, and when there was less at stake in getting each call right. In the loan experiment, officers given strong pay-for-accuracy incentives showed much less of it. Attention and incentives shrink the bias, but they don't make it go away on their own.

Where else this shows up

• Academic and grant-funded research. Anyone scoring things in sequence is exposed: grant reviewers working through a stack of proposals, coders classifying interview transcripts, clinicians rating patient outcomes, graders marking exams. If the order of cases is fixed, say alphabetical or by date received, a rater's drift can line up with some real characteristic of the cases and masquerade as a finding. Randomize the order each rater sees, and where you can, have two raters work through the cases in different orders.
• Non-profit program evaluation. Intake staff deciding who is eligible, caseworkers rating family risk, and site visitors scoring program fidelity all make decision after decision in a row. If a caseworker has just flagged two high-risk families, the third may get the benefit of the doubt it didn't earn. In an evaluation, that kind of noise can blur the difference between groups or create one where none exists. It's worth checking whether ratings depend on the previous rating before you build anything on them.
• AI and LLM evaluation. Human annotators labeling model outputs one after another are prone to the same drift: after a run of “acceptable” labels, a borderline response starts to feel like it should fail. When those labels become your ground truth, the bias gets baked into every accuracy number you report. LLM-as-judge setups that score several responses in one prompt can show their own order effects. Shuffle items for every annotator, hide their previous labels, and test for dependence between consecutive judgments as a standard part of your annotation QA.

What to ask for instead

Whenever a set of decisions or ratings was made in sequence by people, ask one question: does each decision depend on the one before it? It's a quick check. Take the ratings in the order they were made and see whether the previous outcome predicts the current one after accounting for the case itself. In a well-behaved process, it shouldn't. If it does, the fix is usually procedural rather than statistical: randomize the order, break long sessions into shorter ones, and blind raters to their own recent calls. The asylum seekers in Chen, Moskowitz and Shue's data didn't get to choose where they fell in the queue. Your data's cases don't either.

If your study, evaluation or annotation pipeline depends on people making judgment calls one after another, and you want to know whether the order is quietly shaping the results, talk to us.

Related reading

• The Tallest Parents Never Had the Tallest Children — the true version of “things even out”: extreme results drift back toward average, but no single outcome is ever owed a correction.
• The Answer a Thousand PhDs Called Wrong — another case where confident, trained people let intuition about chance override the arithmetic.

Sources and further reading

• Chen, D. L., Moskowitz, T. J., & Shue, K. (2016). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires. Quarterly Journal of Economics, 131(3), 1181–1242.
• National Bureau of Economic Research. (2016, June). The gambler's fallacy. NBER Digest.

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