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Consistency
Geometric Consistency Index (GCI) - Log-quadratic consistency measure for PCMs
Pairwise consistency index - geometric mean priority based
Aguarón, J., Moreno-Jiménez, J.M.2003doi:10.1016/S0377-2217(02)00255-2 ↗
Overview
Use size-dependent thresholds: n=3→0.31, n=4→0.35, n≥5→0.37. GCI is preferred over CR when weights are derived via the geometric mean (LLSM) rather than the eigenvector.
- Output
- Consistency Score, lower is better
- Data
- Crisp, positive reciprocal
- Size
- 3+ alternatives, 3-9 criteria works best
- Used for
- Multi-criteria decision making, AHP, pairwise comparison
Fits when / Look elsewhere when
Fits when
- •Continuous and differentiable
- •Compatible with geometric mean priority derivation
- •Size-specific thresholds available
Look elsewhere when
- •Saaty eigenvector weights are used - Saaty CR is then more coherent
Assumptions to verify
- PCM entries are positive and reciprocal
- Weights derived via geometric mean (LLSM)
Limitations
- •Thresholds approximate (Monte Carlo derived)
- •Less widely recognized than Saaty CR in practice
Edge cases and pitfalls
Using Saaty thresholds (0.1) for GCI - they are different scales.
GCI=0 requires exact consistency, not just low CR.
Works with
How to cite
Aguarón, J.; Moreno-Jiménez, J.M. (2003). The geometric consistency index: Approximated thresholds. European Journal of Operational Research. https://doi.org/10.1016/S0377-2217(02)00255-2
System ID, as it appears in reports and the API
CONSISTENCY-GCI