HE/4
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 mean_absolute_deviation(numbers: List[float]) -> float:
""" For a given list of input numbers, calculate Mean Absolute Deviation
around the mean of this dataset.
Mean Absolute Deviation is the average absolute difference between each
element and a centerpoint (mean in this case):
MAD = average | x - x_mean |
>>> mean_absolute_deviation([1.0, 2.0, 3.0, 4.0])
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 mean_absolute_deviation(numbers: List[float]) -> float:
""" For a given list of input numbers, calculate Mean Absolute Deviation
around the mean of this dataset.
Mean Absolute Deviation is the average absolute difference between each
element and a centerpoint (mean in this case):
MAD = average | x - x_mean |
>>> mean_absolute_deviation([1.0, 2.0, 3.0, 4.0])
1.0
"""
mean = sum(numbers) / len(numbers)
return sum(abs(x - mean) for x in numbers) / len(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 MAD formula and passes the provided doctest example ([1.0, 2.0, 3.0, 4.0] → 1.0). The logic is sound: it computes the mean, then returns the average of absolute deviations. However, the solution has a critical edge case bug: it will crash with a ZeroDivisionError on an empty list, since both `sum(numbers) / len(numbers)` and the final division by `len(numbers)` will fail when len(numbers) == 0. The task description does not explicitly specify how to handle empty input, but this is a plausible edge case that a robust solution should address. The code is otherwise clear and idiomatic.
The solution correctly computes the mean, then computes the average of absolute deviations from the mean. It matches the doctest example ([1,2,3,4] → mean=2.5, MAD=1.0) and handles general cases correctly. The implementation is concise, idiomatic Python. The only unhandled edge case is an empty list (division by zero), but the task doesn't specify behavior for empty input and the docstring implies a non-empty list.
The solution correctly implements the Mean Absolute Deviation (MAD) calculation as specified in the task. It computes the mean of the input list and then calculates the average of the absolute differences from the mean. The provided example in the docstring matches the expected output. The code is clear and idiomatic, handling the task as intended without any apparent edge case issues.