# Mutual Conversion Between Preference Maps And Cook-Seiford Vectors

## TL;DR

This paper demonstrates the equivalence between preference maps and Cook-Seiford vectors in group decision making, providing formulas for mutual conversion and discussing their consistency and potential applications.

## Contribution

It introduces explicit transformation formulas between preference maps and Cook-Seiford vectors, establishing their equivalence for ties-permitted ordinal rankings.

## Key findings

- Preference maps and Cook-Seiford vectors are equivalent representations.
- Explicit formulas for mutual conversion are provided.
- The methods are illustrated with examples and potential applications are discussed.

## Abstract

In group decision making, the preference map and Cook-Seiford vector are two concepts as ways of describing ties-permitted ordinal rankings. This paper shows that they are equivalent for representing ties-permitted ordinal rankings. Transformation formulas from one to the other are given and the inherent consistency of the mutual conversion is discussed. The proposed methods are illustrated by some examples. Some possible future applications of the proposed formulas are also pointed out.

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Source: https://tomesphere.com/paper/1812.03566