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Consistency
Harmonic Consistency Index (HCI) - Harmonic-mean eigenvalue approximation for PCMs
Pairwise consistency index - harmonic mean eigenvalue based
Stein, W.E., Mizzi, P.J.2007doi:10.1016/j.ejor.2005.10.057 ↗
Overview
HCI < 0.1 is acceptable. HCI ≤ CI always - if HCI is acceptable but CI is not, the inconsistency is concentrated in a few extreme entries. Use HCI alongside CI for a fuller picture.
- 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
Fits when / Look elsewhere when
Fits when
- •Conservative lower bound on CI
- •Robust to single extreme outlier entries
- •Computationally simple (no eigenvalue required)
Look elsewhere when
- •As sole consistency criterion - use alongside CI or GCI
Assumptions to verify
- PCM entries are positive and reciprocal
- Geometric mean priority vector computed
Limitations
- •Less widely known than Saaty CR in practice
- •Thresholds same as Saaty (no size-specific calibration)
Edge cases and pitfalls
Using HCI instead of CI unconditionally - HCI is more conservative, so HCI>0.1 is a strong inconsistency signal.
Forgetting that HCI uses the geometric mean priority vector, not the eigenvector.
Works with
How to cite
Stein, W.E.; Mizzi, P.J. (2007). The harmonic consistency index for the analytic hierarchy process. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2005.10.057
System ID, as it appears in reports and the API
CONSISTENCY-HCI