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Rank Reversal Explained

'Rank Reversal' is an instability phenomenon that occurs while ranking products evaluated on multiple parameters, with  methodologies such as weighted sum (scorecard method). An example of such ranking instability is described next, for a wine selection scenario:

Assuming an expert ranks a set of 50 red French wines on multiple attributes. Top 3 wines recommended by the scorecard model are:

1. Chateau Margaux

2. Bordeaux Graves

3. Cheval Blanc

Then, 2 bottles of poor quality table wine are added (new shipment). There are 52 bottles to choose from and the scorecard methodology is run again.

The new ranked results of the scorecard are:

1. Bordeaux Graves

2. Cheval Blanc

3.Chateau Margaux.

Why is this change? As the poor quality wines should not impact the top 3!.

With MAARS, out of the 50 and 52 sets, the top 3 remain stable:

1. Cheval Blanc

2. Chateau Latour

3. Chateau Margaux

Moreover, with MAARS, not only the top 3 wines remain the same after the introduction of 2 poor wine bottles, but it also does not overlook Chateau Latour, which was part of the original 50 bottles and is much better than Bordeaux Graves-an average type of wine.

The above example is a very basic one that shows how such Rank Reversal instability happens (here top 3 but could be top15, top 45 etc.). For big financial data,  the instability of methods other than MAARS can be quite significant, giving the end-user sub-optimal choices, whereas with MAARS, the end-user is assured not to miss the best opportunities.

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