# kemenyd: Kemeny distance In ConsRank: Compute the Median Ranking(s) According to the Kemeny's Axiomatic Approach

## Description

Compute the Kemeny distance of a data matrix containing preference rankings, or compute the kemeny distance between two (matrices containing) rankings.

## Usage

 `1` ```kemenyd(X, Y = NULL) ```

## Arguments

 `X` A N by M data matrix, in which there are N judges and M objects to be judged. Each row is a ranking of the objects which are represented by the columns. If there is only X as input, the output is a square distance matrix `Y` A row vector, or a n by M data matrix in which there are n judges and the same M objects as X to be judged.

## Value

If there is only X as input, d = square distance matrix. If there is also Y as input, d = matrix with N rows and n columns.

## Author(s)

Antonio D'Ambrosio antdambr@unina.it

## References

Kemeny, J. G., & Snell, L. J. (1962). Preference ranking: an axiomatic approach. Mathematical models in the social sciences, 9-23.

`tau_x` TauX rank correlation coefficient
 ```1 2 3 4 5``` ```data(Idea) RevIdea<-6-Idea ##as 5 means "most associated", it is necessary compute the reverse #ranking of each rankings to have rank 1 = "most associated" and rank 5 = "least associated" KD<-kemenyd(RevIdea) KD2<-kemenyd(RevIdea[1:10,],RevIdea[55,]) ```