Implement smooth weighted scores without moving the chart scale

1. Separate three different objects

Keep the model’s base scores, its original vote and the user’s fit ranking as separate data. A slider should change the fit calculation, not claim that a provider reconsidered its opinion. Define the neutral slider position as balanced. In the implementation below, the slider runs from minus one hundred to one hundred and maps exponentially to a weight from one half to two. This provides a symmetric middle on the importance scale without exposing confusing multiplier labels as the main interface.

2. Calculate totals on shared valid dimensions

A weighted mean remains bounded by valid base scores when all weights are positive. If any option lacks a score in a dimension, exclude that dimension from every option’s total for this view. Do not quietly insert zero, and do not divide each product by a different set of weights. With no shared dimensions, return no ranking rather than manufacturing a tie at zero. The example preserves a genuine zero as a numeric score and includes tests for the important edge cases.

import math

def weight(position):
    return 2 ** (max(-100, min(100, position)) / 100)

def totals(rows, weights):
    valid = [all(type(v) in (int,float) and math.isfinite(v) for v in row) for row in rows]
    denominator = sum(w for w, ok in zip(weights, valid) if ok)
    if not denominator:
        return None
    return [sum(row[j]*w for row,w,ok in zip(rows,weights,valid) if ok)/denominator
            for j in range(len(rows[0]))]

def profile(score, position):
    if score is None:
        return None
    s = max(0, min(100, score))
    p = max(-1, min(1, position/100))
    return max(0, min(100, s + .25*p*s*(1-s/100)))

assert weight(0) == 1 and weight(100) == 2
assert totals([[90,80],[None,95]], [1,2]) == [90,80]
assert totals([[None,80]], [1]) is None
assert totals([[0,80]], [1]) == [0,80]
assert 90 < profile(90,100) < 100
print([round(x,1) for x in totals([[90,80],[80,95]], [1,weight(30)])])

3. Keep the grid fixed

A chart’s grid must represent the same zero-to-one-hundred scale before and after an adjustment. If importance is also reflected in a polygon profile, label that profile as a display transform and retain the original score in the tooltip. The bounded transform in the example changes a point gently and cannot exceed the outer scale. Missing points should be omitted, with only adjacent known segments connected. Do not draw a closed polygon through the center to represent an unknown value; that visually claims a real zero.

4. Test ranking sensitivity and reversibility

Use fixtures where two products trade advantages across dimensions, then vary one slider in small steps. Check bounds, missing-data behavior and exact recovery after reset. Confirm that adjusting a control produces no model request. Keep a narrow numerical lead visually different from a broad advantage, and explain when the result is sensitive to preferences. The math does not make subjective AI scores into laboratory measurements. It makes the consequences of a user preference explicit and reproducible.