university of bergamo, italy - ugent · 19 2, 7, 7, 8, 9, 9 common sense: 8 arithmetic mean: 7...
TRANSCRIPT
![Page 1: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/1.jpg)
Gianfranco Gambarelli
University of Bergamo, Italy
![Page 2: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/2.jpg)
25
BARAlexei
Nemov
Athens 2004
![Page 3: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/3.jpg)
- Gymnastics
- Diving
- Figure skating
- Synchronized swimming
- ...
24
SPORTS:
APPLICATIONS
BANKING:
- LIBOR
- EURIBOR
- EONIASWAP
- EUREPO
- ...
EVALUATION OF PROJECTS
…………..
![Page 4: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/4.jpg)
23
2, 7, 7, 8, 9, 9
Common Sense:
8
![Page 5: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/5.jpg)
Vaulting
Arithmetic Mean
2, 7, 7, 8, 9, 9
22
7
![Page 6: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/6.jpg)
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
21
7.75
7.5
![Page 7: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/7.jpg)
Rhythmic Gymn. 4 j.
Median
2, 7, 7, 8, 9, 9
7.5
20
![Page 8: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/8.jpg)
19
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
![Page 9: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/9.jpg)
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.
18
![Page 10: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/10.jpg)
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
17
![Page 11: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/11.jpg)
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
![Page 12: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/12.jpg)
Gambarelli, G. (2008) “The Coherent Majority Average
for juries’ evaluation processes”
Journal of Sport Sciences
15
BANKING:
- LIBOR
- EURIBOR
- EONIASWAP
- EUREPO
- ...
![Page 13: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/13.jpg)
14
![Page 14: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/14.jpg)
13
Execution Artistry Difficulty
THE NEW PROBLEM (sports)
![Page 15: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/15.jpg)
12
Environmental
costs
Building
Costs
Disease
Costs
THE NEW PROBLEM (project eval.)
![Page 16: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/16.jpg)
11
Country AthleteJudges
1I 7 7 4 2
II
2 I
3 I
4 I
5 I
6 I
1 2 3 4
![Page 17: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/17.jpg)
10
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
![Page 18: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/18.jpg)
9
1) How to identify collusions in an objective
way
2) How to take into account it to build a fair
average
![Page 19: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/19.jpg)
8
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
![Page 20: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/20.jpg)
…
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.
7
Most Reliable
Judges
![Page 21: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/21.jpg)
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
6
Regarding our example:
![Page 22: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/22.jpg)
Anti-Collusion Average
the arithmetic mean of the scores
that have been assigned
by the most reliable judges
5
![Page 23: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/23.jpg)
By means of ACA
the judges are pushed
to work properly
in order to avoid
their votes being eliminated
4
![Page 24: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/24.jpg)
3
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.
![Page 25: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/25.jpg)
![Page 26: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/26.jpg)
1
Gambarelli, G., G. Iaquinta and M. Piazza (2012)
“Anti-Collusion Indices and averages for the evaluation of
performances and juries”
Journal of Sport Sciences
![Page 27: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/27.jpg)
![Page 28: University of Bergamo, Italy - UGent · 19 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](https://reader034.vdocument.in/reader034/viewer/2022052012/60286cf42725f655612c842f/html5/thumbnails/28.jpg)