University of Bergamo, Italy - UGent · 19 2, 7, 7, 8, 9, 9 Common Sense: 8 Arithmetic Mean: 7...
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Gianfranco Gambarelli University of Bergamo, Italy
Transcript of University of Bergamo, Italy - UGent · 19 2, 7, 7, 8, 9, 9 Common Sense: 8 Arithmetic Mean: 7...
Gianfranco Gambarelli
University of Bergamo, Italy
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BARAlexei
Nemov
Athens 2004
- Gymnastics
- Diving
- Figure skating
- Synchronized swimming
- ...
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SPORTS:
APPLICATIONS
BANKING:
- LIBOR
- EURIBOR
- EONIASWAP
- EUREPO
- ...
EVALUATION OF PROJECTS
…………..
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2, 7, 7, 8, 9, 9
Common Sense:
8
Vaulting
Arithmetic Mean
2, 7, 7, 8, 9, 9
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7
Diving 5 judges
trimmed mean (but 2)
2, 7, 7, 8, 9, 9
Diving 7 judges
trimmed mean (but 4)
2, 7, 7, 8, 9, 9
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7.75
7.5
Rhythmic Gymn. 4 j.
Median
2, 7, 7, 8, 9, 9
7.5
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2, 7, 7, 8, 9, 9
Common Sense: 8
Arithmetic Mean: 7
Trimmed mean (but 2): 7.75
Trimmed mean (but 4): 7.50
Median: 7.50
The Coherent Majority Average
The goals:
- correct evaluation
- incentive to judges.
The assumptions:
- the majority of scores is reliable
- they relate well to those scores
which are closest to them.
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6 judges → majority = 4
2, 7, 7, 8, 9, 9
└─────┘
8-2 = 6
└─────┘
9-7 = 2
└─────┘
9-7 = 2
Minimum difference: 2
Corresponding scores: 7,7,8,9,9
Arithmetic mean of such scores (= CMA): 8
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Common Sense Recovered
2, 7, 7, 8, 9, 9
Common Sense: 8
Arithmetic Mean: 7
Trimmed mean (but 2): 7.75
Trimmed mean (but 4): 7.50
Median: 7.50
Coherent Majority Av.: 816
Gambarelli, G. (2008) “The Coherent Majority Average
for juries’ evaluation processes”
Journal of Sport Sciences
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BANKING:
- LIBOR
- EURIBOR
- EONIASWAP
- EUREPO
- ...
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13
Execution Artistry Difficulty
THE NEW PROBLEM (sports)
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Environmental
costs
Building
Costs
Disease
Costs
THE NEW PROBLEM (project eval.)
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Country AthleteJudges
1I 7 7 4 2
II
2 I
3 I
4 I
5 I
6 I
1 2 3 4
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Country AthleteJudges
1I 7 7 4 2
II 7 7 4 4
2 I 6 7 4 4
3 I 6 8 10 9
4 I 6 6 9 9
5 I 7 7 4 4
6 I 7 6 3 5
1 2 3 4
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1) How to identify collusions in an objective
way
2) How to take into account it to build a fair
average
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Index of self-valuation of p:
average scores awarded to p by judges that belong to p
average scores that other judges have awarded to p
Index of others’ valuation of p:
average scores awarded by judges of p to the perform. of the other teams
average scores awarded by other judges to the perform. of the other teams
For each coalition p:
The idea
Index of coalitional collusion of p =index of self-valuation of p
index of other’s valuation of p
…
1.86
1.07
0.97
1.18
1.04
2.55
1.48
1.31
1.67
1.70
= 1.86
= 2.55
= 1.86
= 2.55
= 2.55
= 1.86
= 1.70
= 1.67
= 1.48
= 1.31
= 1.18
= 1.07
= 1.04
= 0.97
1°
2°
Coalitional c.i.Ordered
Coalitional c.i.
Ordered
Individual c.i.
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Most Reliable
Judges
Country AthleteJudges
1I 7 7 4 2
II 7 7 4 4
2 I 6 7 4 4
3 I 6 8 10 9
4 I 6 6 9 9
5 I 7 7 4 4
6 I 7 6 3 5
1 2 3 4 ACA
7
7
6.5
7
6
7
6.5
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Regarding our example:
Anti-Collusion Average
the arithmetic mean of the scores
that have been assigned
by the most reliable judges
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By means of ACA
the judges are pushed
to work properly
in order to avoid
their votes being eliminated
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Bertini, C., G. Gambarelli and A. Uristani (2010)
"Collusion Indices and an Anti-collusion Average”
Preferences and decisions: models and applications,
Studies in Fuzziness and Soft Computing, Springer Verlag.
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Gambarelli, G., G. Iaquinta and M. Piazza (2012)
“Anti-Collusion Indices and averages for the evaluation of
performances and juries”
Journal of Sport Sciences
