iwquickcons | R Documentation |

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

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

`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 |

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.

a "list" containing the following components:

Consensus | the Consensus Ranking | |

Tau | averaged item-weighted TauX rank correlation coefficient | |

Eltime | Elapsed time in seconds |

Alessandro Albano alessandro.albano@unipa.it

Antonella Plaia antonella.plaia@unipa.it

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

`consrank`

```
#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)
```

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