# An Alternative Globalization Barometer for Investigating the Trend of Globalization
## 2 Materials and Methods
### Methods  
#### 2.4.1 The CRITIC Method  
Two major weighting systems are used in related studies: The objective and subjective weighting methods [33]. The former is dataset-driven, while the latter is expert-driven. In order to eliminate subjective biases, our work employs the CRITIC method to aggregate  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Primary Indicators** & **Secondary Indicators** & **Tertiary Indicators** & **Source** \\ \hline \multirow{8}{*}{Social} & \multirow{2}{*}{Informational} & _de facto_ & Used internet bandwidth & ITU ICT-Eye \\  & & _de jure_ & Internet access & ITU ICT-Eye \\ \cline{2-4}  & & \multirow{2}{*}{Interpersonal} & \multirow{2}{*}{_de facto_} & International tourism & World Bank WDI \\  & & & International students & World Bank WDI \\  & & & Migration & World Bank WDI \\ \cline{2-4}  & & _de jure_ & Freedom to visit & DEMIG VISA \\  & & & International airports & CIA World Factbook * \\ \cline{2-4}  & \multirow{2}{*}{Technological} & \multirow{2}{*}{_de facto_} & International patents & World Bank WDI \\  & & & High technology exports & World Bank WDI \\ \cline{2-4}  & & _de jure_ & Global innovation index & GII \\ \cline{2-4}  & & \multirow{2}{*}{Cultural} & \multirow{2}{*}{_de facto_} & Trade in printed goods & UN Comtrade \\  & & & International trademarks & WIPO IP Portal \\ \cline{2-4}  & & \multirow{2}{*}{_de jure_} & Social tolerance index & World Value Survey \\  & & & Language popularity index & Ethnologue * \\ \hline \multirow{8}{*}{Political} & \multirow{2}{*}{International Cooperation} & \multirow{2}{*}{_de facto_} & Foreign affairs agencies & Lowy Global \\  & & & Diplomacy \\ \cline{1-1} \cline{3-4}  & & _de jure_ & International organizations & CIA World Factbook * \\ \cline{1-1} \cline{3-4}  & & & International treaties & UN Treaty Collection * \\ \cline{1-1} \cline{2-4}  & \multirow{2}{*}{Global governance} & \multirow{2}{*}{_de facto_} & Speech contribution in UN & UN Digital Library * \\ \cline{1-1}  & & _de jure_ & UN peacekeeping contribution & UN Peacekeeping * \\ \hline \hline \end{tabular}  
* Indicators manually collected and calibrated from accessible databases.  
\end{table}
Table 1: _Cont._our indicators. This method is based on evaluating the comparative strength between indicators and the deviation of indicators to determine the weights of indicators.  
Consider a normalized dataset represented by matrix \(M\):  
\[M=\begin{bmatrix}x_{11}&x_{12}&\cdots&x_{1n}\\ x_{21}&x_{22}&\cdots&x_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ x_{m1}&x_{m2}&\cdots&x_{mn}\end{bmatrix} \tag{1}\]  
where \(m\) denotes the number of observations, and \(n\) denotes the number of indicators under the same category.  
While determining the weights of a specific indicator, both standard deviation and its correlation between indicators are considered. In this regard, the weights are obtained as follows:  
\[w_{j}=\frac{C_{j}}{\sum_{j=1}^{n}C_{j}} \tag{2}\]  
where \(C_{j}\) denotes the quantity of information \(j\)-th indicator contains, which is determined as:  
\[C_{j}=\sigma_{j}\cdot\sum_{k=1}^{n}\left(1-r_{kj}\right) \tag{3}\]  
where \(\sigma_{j}\) represents the standard deviation, and \(r_{kj}\) represents the correlation coefficient between indicator \(k\) and \(j\).