FASTcons: FAST algorithm to find consensus (median) ranking according the Kemeny's axionatic approach

Description

FAST algorithm to find consensus (median) ranking defined by Amodio, D'Ambrosio and Siciliano (2015). It returns at least one of the solutions. If there are multiple solutions, sometimes it returns all the solutions, sometimes it returns some solutions, always it returns at least one solution.

Usage

FASTcons(X, Wk = NULL, maxiter = 50, FULL=FALSE)

Arguments

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. Alternatively X can contain the rankings observed only once in the sample. In this case the argument

Optional: the frequency of each ranking in the data

maxiter

maximum number of iterations: default = 50.

FULL

Default FULL=FALSE. If FULL=TRUE, the searching is limited to the space of full rankings. In this case, the data matrix must contain full rankings.

Value

ConsensusConsensus ranking
TauTau extended rank correlation coefficient
EltimeElapsed time in seconds

References

Amodio, S., D'Ambrosio, A. & Siciliano, R (2015). Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach. European Journal of Operational Research. DOI: 10.1016/j.ejor.2015.08.048.

Examples

Run this code

#data(EMD)
#X=EMD[,1:15]
#Wk=matrix(EMD[,16],nrow=nrow(X))
#CR=FASTcons(X,Wk,maxiter=100)
#These lines produce all the three solutions in less than a minute.

data(sports)
CR=FASTcons(sports,maxiter=10)