Kardi Teknomo
Kardi Teknomo Kardi Teknomo Kardi Teknomo


Visit Tutorials below:
Adaptive Learning from Histogram
Adjacency matrix
Analytic Hierarchy Process (AHP)
ArcGIS tutorial
Arithmetic Mean
Bayes Theorem
Bootstrap Sampling
Bray Curtis Distance
Break Even Point
Chebyshev Distance
City Block Distance
Conditional Probability
Continued Fraction
Data Analysis from Questionnaire
Data Revival from Statistics
Decimal to Rational
Decision tree
Difference equations
Digital Root
Discriminant analysis
Eigen Value using Excel
Euclidean Distance
Euler Integration
Euler Number
Excel Iteration
Excel Macro
Excel Tutorial
Feasibility Study
Financial Analysis
Generalized Inverse
Generalized Mean
Geometric Mean
Ginger Bread Man and Chaos
Graph Theory
Growth Model
Hamming Distance
Harmonic Mean
Hierarchical Clustering
Independent Events
Incident matrix
Jaccard Coefficient
Kernel basis function
Kernel Regression
k-Means clustering
K Nearest Neighbor
LAN Connections Switch
Learning from data
Lehmer Mean
Linear Algebra
Logarithm Rules
Mahalanobis Distance
Market Basket Analysis
Mean Absolute Deviation
Mean and Average
Mean, median, mode
Minkowski Distance
Minkowski Mean
Monte Carlo Simulation
Multi Agent System
Multicriteria decision making
Mutivariate Distance
Newton Raphson
Non-Linear Transformation
Normalization Index
Normalized Rank
Ordinary Differential Equation
Page Rank
Power rules
Prime Factor
Prime Number
Q Learning
Quadratic Function
Rank Reversal
Recursive Statistics
Regression Model
Reinforcement Learning
Root of Polynomial
Scenario Analysis
Sierpinski gasket
Sieve of Erastosthenes
Similarity and Distance
Solving System Equation
Standard deviation
Summation Tricks
Support Vector Machines
System dynamic
Time Average
Tower of Hanoi
Vedic Square
Visual Basic (VB) tutorial
What If Analysis

Rank Reversal

By Kardi Teknomo, PhD.

Share this: Google+

Click here to purchase more complete e-book of this rank reversal tutorial.

In this simple tutorial I will show that rank aggregation will lead to rank reversal compared to score aggregation.

Suppose 5 judges have to evaluate 10 types of items. Each judge gives score 1 to 100 for each item. Here is an example of their judgments.


Since all judges are considered equally experts, their weights are equal. Thus, we can either sum their scores or take average of their scores. Our goal in evaluating the items is to rank the items. Table below show the aggregation results and we rank the average (or the sum) of the scores.

Score aggregation

Now suppose we have another scenario that the judges want to use their rank instead of their scores. In this case, each judge will rank their scores. Below are their ranks based on the scores above.


To aggregate the rank, they use the same way as aggregating the scores that is using sum or average. However, this time, we aggregate the ranks instead of the scores. Then, they sort the rank aggregation using based on minimum rank aggregation.

Rank aggregation

Notice that the rank based on the aggregation of scores is not the same as the rank based on the aggregation of rank. Some item will have reverse order. That is what we called as rank reversal . In general, rank reversal is the rule of rank aggregation. The similarity between rank of scores and rank of rank is just incidental. In the example above, item 2 suppose to have rank 9 but using rank aggregation, it becomes rank 8. On the other hand, item 4 suppose to have rank 7 but using rank aggregation, now it goes down to rank 9.

Rank reversal

The simple lesson is: for group decision, use score aggregation, and not rank aggregation because it may lead to rank reversal.

With only $4.99, you will get the more complete e-book of this rank reversal tutorial. Click here to purchase it NOW!

Rate this tutorial

See Also: AHP, Multi Criteria Decision Making

This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. (2009) Rank Reversal.


© 2007 Kardi Teknomo. All Rights Reserved.
Designed by CNV Media