# Quick algorithm to find up to 4 solutions to the consensus ranking problem

### Description

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

### Usage

1 |

### 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 |

`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. In this case, the data matrix must contain full rankings. |

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

### Value

`Consensus ` |
Consensus ranking |

`Tau ` |
Tau extension rank correlation coefficient |

### Author(s)

Antonio D'Ambrosio <antdambr@unina.it> and Sonia Amodio <sonia.amodio@unina.it>

### 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.

### See Also

FASTcons

EMCons

### Examples

1 2 |