HE/21
This is one (task, candidate response) pair flowing through the full PANOPTES pipeline. Each section below is a stage of the analysis: the task itself, the candidate solution being evaluated, every judge's score + rationale, the sampling-pass dispersion that captures within-judge noise, and the uncertainty-quantification metrics computed on top.
The function signature + docstring presented to both the model under test and to every judge.
from typing import List
def rescale_to_unit(numbers: List[float]) -> List[float]:
""" Given list of numbers (of at least two elements), apply a linear transform to that list,
such that the smallest number will become 0 and the largest will become 1
>>> rescale_to_unit([1.0, 2.0, 3.0, 4.0, 5.0])
[0.0, 0.25, 0.5, 0.75, 1.0]
"""
The full solution every judge is grading. For these runs the candidate is the reference solution prepended with the task signature so it parses as a complete program.
from typing import List
def rescale_to_unit(numbers: List[float]) -> List[float]:
""" Given list of numbers (of at least two elements), apply a linear transform to that list,
such that the smallest number will become 0 and the largest will become 1
>>> rescale_to_unit([1.0, 2.0, 3.0, 4.0, 5.0])
[0.0, 0.25, 0.5, 0.75, 1.0]
"""
min_number = min(numbers)
max_number = max(numbers)
return [(x - min_number) / (max_number - min_number) for x in numbers]
One call per judge at temperature=0. This is the "best single guess" each judge has. Disagreement here is structural. The judges literally see this candidate differently.
n draws per judge at temperature=1. Dots are individual draws; vertical bar is the mean; shaded band is ±1σ. Wide band = the judge is uncertain even with itself; narrow band = it's consistent.
Three statistical methods computed on top of the raw scores above. Each one tells you something different about how much to trust the headline number.
How to read these: self-consistency = does the judge agree with itself when resampled? Narrower CI means more consistent. Semantic entropy = do the judge's rationales cluster into one meaning, or several? Higher entropy means the judge is internally conflicted about why. Decomposition = how much of the total variance comes from within-judge sampling noise (aleatoric, hard to fix) vs between-judge disagreement (epistemic, fixable by calling more judges).
The natural-language explanation each judge gave alongside its score. These are produced via tool-use structured output, so the score and the rationale are guaranteed to come from the same forward pass.
The solution correctly implements the linear rescaling formula for the canonical example: (x - min) / (max - min) maps the minimum to 0 and maximum to 1. However, it has a critical bug: when all numbers are identical (min == max), the denominator becomes zero, causing a ZeroDivisionError. The task states "at least two elements" but doesn't explicitly exclude the case where all elements are equal—a plausible edge case. The solution passes the given doctest but fails on realistic edge cases like [5.0, 5.0, 5.0] or [1.0, 1.0]. The code is otherwise clear and idiomatic, but the unhandled division-by-zero error is a pervasive bug that would surface on realistic input.
The solution correctly implements the linear rescaling: it finds min and max, then maps each element to (x - min) / (max - min). This produces the correct output for the given example [1.0, 2.0, 3.0, 4.0, 5.0] → [0.0, 0.25, 0.5, 0.75, 1.0]. The task specifies "at least two elements," so the edge case of all-equal elements (which would cause division by zero) is technically not excluded by the spec but is an implicit concern. Since the prompt guarantees at least two elements but doesn't explicitly guarantee distinct values, there's a minor unhandled edge case (all elements equal → ZeroDivisionError). Otherwise the solution is clean, idiomatic, and correct.
The solution correctly implements the rescaling of the input list such that the smallest number becomes 0 and the largest becomes 1. It passes the provided example and handles edge cases, such as when the input list contains only two elements. The code is clear and idiomatic, using list comprehension effectively.