MEDIAN-RANKING - Median ranking - per-alternative median rank

Overview

Input: rank matrix (rows=alts, cols=rankings, cell=rank 1..m). Source: Orakçı 2024 §1.8.8.

Output

rank position, lower is better

Data

Crisp, complete rank

Size

2+ alternatives, 3-12 criteria works best

Used for

Rank aggregation, social choice, preference fusion

How it works

1. 1

   For each alternative, compute the median of its ranks across all rankings. Lower median = better.

   $$media{n}_i=median{r}_{i}1,r_{i}2,\dots ,r_{i}n;rankascending$$

   Orakçı 2024 §1.8.8

Fits when / 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

• Applying MEDIAN-RANKING without verifying this assumption.

  Requirement: Input is a rank matrix (1=best, m=worst per voter)

• Applying MEDIAN-RANKING without verifying this assumption.

  Requirement: Each voter ranks all alternatives

• Using MEDIAN-RANKING when: Cardinal preferences important → use a MAUT method.

  An alternative method is recommended in this situation.

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