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C. Valsecchi and R. Todeschini
due to the progressive smoothing of the tournament table (formula 3) which lead to
smaller entropy values.
The PCA was then performed using the PWR rankings for the retained thresholds
(i.e. thresholds leading to a ranking with a correlation lower than 0.995 with the
others). The CPWR ranking plots are shown in Fig. 2. It is evident that the European
countries (green circles) are in general on the top of the CPWR plots, together
with some Central-American countries (black circles) such as Costa Rica (CRI)
and Cuba (CUB) and two Oceania countries (purple circles): Australia (AUS) and
Fig. 2 Consensus ranking for all the countries represented by CPWR with equal (a) and
proportional (b) initial weights for the indicators. Regression coefficients at threshold 0.5 for equal
(c) and proportional (d) initial weights (the coefficient of determination R 2 is equal to 0.92 and
0.89 for the equal and proportional weight initializations, respectively)
C. Valsecchi and R. Todeschini
due to the progressive smoothing of the tournament table (formula 3) which lead to
smaller entropy values.
The PCA was then performed using the PWR rankings for the retained thresholds
(i.e. thresholds leading to a ranking with a correlation lower than 0.995 with the
others). The CPWR ranking plots are shown in Fig. 2. It is evident that the European
countries (green circles) are in general on the top of the CPWR plots, together
with some Central-American countries (black circles) such as Costa Rica (CRI)
and Cuba (CUB) and two Oceania countries (purple circles): Australia (AUS) and
Fig. 2 Consensus ranking for all the countries represented by CPWR with equal (a) and
proportional (b) initial weights for the indicators. Regression coefficients at threshold 0.5 for equal
(c) and proportional (d) initial weights (the coefficient of determination R 2 is equal to 0.92 and
0.89 for the equal and proportional weight initializations, respectively)