a person isn't a weighted average

We're tempted to score people the way we score products, adding up the dimensions and letting a high total cover for a low entry, as if enough talent could outvote a streak of dishonesty.

\[ \begin{aligned} \text{arithmetic mean} &= \frac{9 + 9 + 9 + 0}{4} = 6.75 \\ \text{geometric mean} &= \sqrt[4]{\,9 \cdot 9 \cdot 9 \cdot 0\,} = 0 \end{aligned} \]

the four numbers score one person on ability, ability, ability, and honesty. the arithmetic mean adds them and divides by four, giving 6.75, still impressive. the geometric mean multiplies them and takes the fourth root, and any single zero forces the whole thing to zero. honesty behaves like a factor, not one more column to add up.

A brilliant mind welded to cruelty isn't a strong score with one weak column -- it's a brilliant delivery system for cruelty, and the brilliance makes it worse. The honest model has a few terms that multiply, where one zero takes the whole thing to nothing no matter how large the others grow.