### Abstract

Multidimensional ordinal measurement in a form of problem of a single consensus ranking determination for m rankings of n alternatives is considered in the paper. The Kemeny rule is one of deeply justified ways to solve the problem allowing to find such a linear order (Kemeny ranking) of alternatives that a distance (defined in terms of a number of pair-wise disagreements between rankings) from it to the initial rankings is minimal. But computational experiments outcomes show that the approach can give considerably more than one optimal solutions what argues instability of the measurement procedure. Hence, special efforts to avoid this phenomenon are needed.

Original language | English |
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Title of host publication | 20th IMEKO World Congress 2012 |

Pages | 2071-2074 |

Number of pages | 4 |

Volume | 3 |

Publication status | Published - 2012 |

Event | 20th IMEKO World Congress 2012 - Busan, Korea, Republic of Duration: 9 Sep 2012 → 14 Sep 2012 |

### Other

Other | 20th IMEKO World Congress 2012 |
---|---|

Country | Korea, Republic of |

City | Busan |

Period | 9.9.12 → 14.9.12 |

### Fingerprint

### Keywords

- Consensus relation
- Kemeny ranking problem
- Multiple optimal solutions
- Ordinal scale measurement

### ASJC Scopus subject areas

- Computer Science Applications
- Environmental Engineering
- Biomedical Engineering

### Cite this

*20th IMEKO World Congress 2012*(Vol. 3, pp. 2071-2074)

**Chaotic results of multidimensional ordinal measurements.** / Muravyov, S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*20th IMEKO World Congress 2012.*vol. 3, pp. 2071-2074, 20th IMEKO World Congress 2012, Busan, Korea, Republic of, 9.9.12.

}

TY - GEN

T1 - Chaotic results of multidimensional ordinal measurements

AU - Muravyov, S.

PY - 2012

Y1 - 2012

N2 - Multidimensional ordinal measurement in a form of problem of a single consensus ranking determination for m rankings of n alternatives is considered in the paper. The Kemeny rule is one of deeply justified ways to solve the problem allowing to find such a linear order (Kemeny ranking) of alternatives that a distance (defined in terms of a number of pair-wise disagreements between rankings) from it to the initial rankings is minimal. But computational experiments outcomes show that the approach can give considerably more than one optimal solutions what argues instability of the measurement procedure. Hence, special efforts to avoid this phenomenon are needed.

AB - Multidimensional ordinal measurement in a form of problem of a single consensus ranking determination for m rankings of n alternatives is considered in the paper. The Kemeny rule is one of deeply justified ways to solve the problem allowing to find such a linear order (Kemeny ranking) of alternatives that a distance (defined in terms of a number of pair-wise disagreements between rankings) from it to the initial rankings is minimal. But computational experiments outcomes show that the approach can give considerably more than one optimal solutions what argues instability of the measurement procedure. Hence, special efforts to avoid this phenomenon are needed.

KW - Consensus relation

KW - Kemeny ranking problem

KW - Multiple optimal solutions

KW - Ordinal scale measurement

UR - http://www.scopus.com/inward/record.url?scp=84880405356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880405356&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781627481908

VL - 3

SP - 2071

EP - 2074

BT - 20th IMEKO World Congress 2012

ER -