Gini Coefficient Weighting - inequality-of-discrimination objective weighting

Overview

Gini weight is proportional to the inequality of performance values across alternatives (after normalisation). A criterion where all alternatives perform identically gets G_j=0 → w_j=0. Higher inequality → higher weight. Unlike ENTROPY and SD, uses the Gini coefficient (mean absolute difference) instead of variance or entropy.

Output

Weight, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Any (objective weighting)

How it works

1. 1

   Convert all criteria to benefit direction: for cost, x_ij → (max_k x_kj − x_ij). Normalise by column sum.

   $$p_{ij}=x_{ij}^{+}/\sum _k{x}_{kj}^{+}$$

   Adapted from Gini 1912 (Gini coefficient applied to MCDM normalised column; pending PDF page verification)

2. 2

   Compute Gini coefficient G_j for each criterion column: G_j = (Σ_i Σ_k |p_ij − p_kj|) / (2m² μ_j) where μ_j = mean(p_ij). Normalise: w_j = G_j / Σ G_l.

   $$G_j=\frac{{\sum }_i{\sum }_k|p_{ij}-p_{kj}|}{2m^2{\bar{p}}_j};w_j=G_j/\sum _l{G}_l$$

   Gini 1912 adapted for MCDM (pending PDF page verification)

Look elsewhere when

Assumptions to verify

• Decision matrix exists with measurable criteria
• Sufficient inter-alternative variation per criterion

Edge cases and pitfalls

• Requires non-negative column values after direction conversion. If column contains zeros, G_j computation may still work (μ_j=0 case: assign G_j=0).

Works with

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