iwquickcons {ConsRank}

The item-weighted Quick algorithm to find up to 4 solutions to the consensus ranking problem

Description

The item-weighted Quick algorithm finds up to 4 solutions. Solutions reached are most of the time optimal solutions.

Usage

iwquickcons(X, w, Wk = NULL, full = FALSE, PS = FALSE)

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

w

A M-dimensional row vector (individually weighted items), or a M by M matrix (item similarities)

Wk

Optional: the frequency of each ranking in the data

full

Default full=FALSE. If full=TRUE, the searching is limited to the space of full rankings.

PS

Default PS=FALSE. If PS=TRUE the number of evaluated branches is diplayed

Details

The item-weigthed Quick algorithm finds up the consensus (median) ranking according to the Kemeny's axiomatic approach. The median ranking(s) can be restricted to be necessarily a full ranking, namely without ties.

Value

a "list" containing the following components:

Consensus		the Consensus Ranking
Tau		averaged item-weighted TauX rank correlation coefficient
Eltime		Elapsed time in seconds

Author(s)

Alessandro Albano [e-mail]
Antonella Plaia [e-mail]

References

Amodio, S., D'Ambrosio, A. and Siciliano, R. (2016). Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach. European Journal of Operational Research, 249(2), 667-676.
Albano, A. and Plaia, A. (2021). Element weighted Kemeny distance for ranking data. Electronic Journal of Applied Statistical Analysis, doi: 10.1285/i20705948v14n1p117

See Also

consrank

Examples

#Individually weighted items
data("German")
w=c(10,5,5,10)
iwquickcons(X= German,w= w)

#Item similirity weights
data(sports)
dim(sports)
P=matrix(NA,nrow=7,ncol=7)
P[1,]=c(0,5,5,10,10,10,10)
P[2,]=c(5,0,5,10,10,10,10)
P[3,]=c(5,5,0,10,10,10,10)
P[4,]=c(10,10,10,0,5,5,5)
P[5,]=c(10,10,10,5,0,5,5)
P[6,]=c(10,10,10,5,5,0,5)
P[7,]=c(10,10,10,5,5,5,0)
iwquickcons(X= sports, w= P)