iwquickcons {ConsRank} | R Documentation |

## 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 alessandro.albano@unipa.it

Antonella Plaia antonella.plaia@unipa.it

### 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

### 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)
```

*ConsRank*version 2.1.4 Index]