How a weighted decision matrix works
Put the options down the side and the things that matter across the top. Give each criterion a weight for how much it counts, then score every option on every criterion. An option's total is the sum of weight × score, so a strong score on a heavy criterion counts for more than one on a light criterion.
Total = Σ weight × score; share of maximum = total ÷ (Σ weights × 10)
In the laptop example, Laptop C scores 5, 9, 9 and 8 on price, battery, weight and screen, weighted 5, 4, 3 and 2: 25 + 36 + 27 + 16 = 104 out of a possible 140, or 74%. Laptop B wins on price but loses elsewhere and finishes on 97.
The sensitivity check asks what people forget to ask: how far would one weight have to move to change the answer? If a small change would do it, the options are close, and the decision may hang on something you haven't scored yet.