A stray number can shift an AI model’s estimates

Can an arbitrary number steer an estimate?

Imagine seeing a roulette wheel land on a number before estimating a percentage. The wheel supplies no useful evidence, yet the number can influence human judgments. Behavioral economists call this anchoring: estimates shift toward an initial reference value, even when it is uninformative.

In an arXiv preprint, Felipe Valencia-Clavijo investigates anchoring-like effects in six language models. The study asks two separate questions: does replacing a low number with a high one shift the model’s expected answer, and does it increase the numerical cue’s attributed contribution to answer probabilities?

These are computational experiments, not experiments with human participants. Similar-looking responses do not establish that machines and people use the same cognitive processes.

Measuring possible answers, not sampled replies

The models were GPT-2, GPT-Neo-125M, Falcon-RW-1B, Gemma-2B, Phi-2 and Llama-2-7B. Each received structured prompts introducing a number, asking whether a percentage was above or below it, and requesting an estimate.

A classic question about African countries in the United Nations served as a positive control. Because that famous experiment might appear in training data, it was excluded from aggregate results. The main analysis used five related questions concerning Asian, South American, English-speaking, EU and French-speaking countries in the UN.

Each question was tested with anchors of 10 and 65, and again with a different pair. The alternative pairs ranged from 15–70 to 35–90, always preserving a 55-point gap. This produced ten non-control conditions per model, but the questions remained concentrated on one subject area.

Rather than repeatedly generating responses, the researcher scored every candidate answer from “0%” through “100%.” The probabilities were normalized across those 101 strings, then used to calculate a weighted average called SoftEV.

A rise in SoftEV means that larger numerical answers gained weight within this restricted set. It does not describe the full range of answers a model could freely generate, such as explanations, qualifications or refusals.

Which part of the prompt contributed?

The second analysis divided each prompt into four fields: the scene, comparison question, final estimation question and numerical anchor. It evaluated all 16 combinations of field presence and absence, replacing missing fields with empty strings.

Using a mathematical attribution method called Banzhaf values, the researcher calculated how much adding the anchor field changed each candidate answer’s log-probability, averaged equally across combinations of the other fields. These contributions were then averaged across candidate answers and compared between high and low anchors.

The calculation is exact for the chosen four-field setup: it does not estimate contributions by sampling field combinations. But exact calculation does not make it an explanation of the model’s internal circuitry. The attribution depends on the selected fields, scoring method and deletion procedure.

Answers shifted, but attribution sometimes diverged

Higher anchors generally increased the probability-weighted estimates, although the size of the shift varied substantially. In the standard-anchor question about South American countries, Gemma-2B’s SoftEV rose from 23.43% to 52.13%, a 28.70-percentage-point increase. Phi-2’s corresponding increase was only 1.51 points.

Behavioral shifts and attributional changes did not consistently align. GPT-Neo-125M often assigned greater relative weight to larger answers under high anchors while showing a lower average anchor-field contribution. That is not contradictory: redistributing probability toward higher numbers and increasing average log-probability contributions across all candidates are different measurements.

The proposed Anchoring Bias Sensitivity Score combines both signals with statistical diagnostics and directional agreement. Gemma-2B ranked highest, followed by Phi-2 and Llama-2-7B. This is a ranking under the paper’s composite formula and selected prompts—not a general safety ranking. A lower score does not necessarily mean smaller behavioral shifts.

What the evidence cannot establish

The statistical tests compare candidate-level scores from the same model evaluations, not independent participants or independently sampled experiments. The paper therefore treats their significance levels as conditional diagnostics. The composite ranking inherits that limitation.

Changing questions and anchors also cannot rule out training-data contamination. Nor do these six models and closely related prompts establish how current instruction-tuned systems behave in realistic decisions.

The practical concern is sensitivity to irrelevant numerical context, particularly when models act as simulated research participants or automated evaluators. The study demonstrates that sensitivity in a controlled setting; it does not measure downstream financial, legal or medical harm, or establish a remedy.