KEMIRA - KEmeny Median Indicator Ranks Accordance

Overview

KEMIRA targets situations where the criteria split into two semantically distinct groups (e.g. technical vs social) and several experts disagree on intra-group ordering. The Kemeny-median step produces a single consensus priority per group; the F(X,Y) step picks weights that make the two group-aggregates as balanced as possible. The final ranking is then a simple sum of weighted group scores.

Output

rank position, higher is better

Data

Crisp, complete rank

Size

2+ alternatives, 3-12 criteria works best

Used for

Rank aggregation, social choice, preference fusion

Look elsewhere when

Assumptions to verify

• Input is a rank matrix (1=best, m=worst per voter)
• Each voter ranks all alternatives

Edge cases and pitfalls

• Computational cost: the weight enumeration grows combinatorially. At Δ=0.10 with n_x=4 the book lists 23 vectors; smaller Δ blows up quickly. Use coarser Δ for screening or LP-based optimisation for production runs.

• Multiple Kemeny-median matrices can tie at the minimum distance (the book's case study yields three tied Group-Y candidates). Document the tie-break rule used (e.g. lexicographic on first-listed expert).

Works with

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