## 3 Methodology
### Statistical Analysis of Ambiguities and MCDA  
If discrepancies between \(S_{t}^{G}\) and \(S_{t}^{L}\) towards specific technologies appear in a survey round, further analyses can be carried out to determine the corresponding drivers \(D\subseteq F\). The decision makers may consider these drivers when consolidating \(S_{t}^{G}\) and \(S_{t}^{L}\) according to  
\[S_{t}=h\left(S_{t}^{G},S_{t}^{L},\;D\right)\]  
with a function \(h:\left\{1,\ldots,P\right\}^{2l}\times F\rightarrow\left\{1,\ldots,P\right\} ^{l}\). Exemplarily, the global and local surveys can be consolidated by means of the weighted sum  
\[S_{t}=w_{D}^{G}\cdot S_{t}^{G}+w_{D}^{L}\cdot S_{t}^{L}\]  
where the weights \(w_{D}^{G}\) and \(w_{D}^{L}\) are possibly influenced by the identified drivers \(D\). The consolidated surveys are aggregated over time according to the function \[\gamma:\{1,\ldots,P\}^{|T|\cdot l}\rightarrow\{1,\ldots,P\}^{l}\]  
The final outcome of the surveys is summarized as follows:  
\[S=\gamma\Big{(}S_{1},\ldots,S_{t_{p}}\Big{)}=(s_{1},\ldots,\;s_{l})\]  
with \(s_{j}\in\{1,\ldots,P\}\).  
To identify a suitable SET mix, MCDA is carried out after the surveys are completed. Let  
\[\mathcal{A}=\left\{\mathcal{A}^{1},\ldots,\mathcal{A}^{m}\right\}\]  
be the set of decision alternatives with  
\[\mathcal{A}^{i}=\sum_{k=1}^{l}w_{k}^{i}\mathcal{T}^{k}\]  
and \(w_{k}^{i}\in[0,1]\), \(\sum_{k=1}^{l}w_{k}^{i}=1\). Hence, each alternative represents a specific technological mix. Let  
\[\mathcal{C}=\left\{\mathcal{C}_{1},\ldots\mathcal{C}_{m}\right\}\]  
be the set of criteria that decision makers wish to consider in deciding on an appropriate technological mix. Let \(\mathcal{CC}\in\mathcal{C}\) reflect the respective citizens' opinions on a specific technological mix, which is elaborated on the basis of several survey rounds.  
The score of a decision alternative \(\mathcal{A}^{i}\), \(1\leq i\leq m\), with respect to a criterion \(\mathcal{C}_{j},1\leq j\leq n\), is defined as follows  
\[x\Big{(}\mathcal{A}^{i},\mathcal{C}_{j}\Big{)}:=x_{ij}\]  
The values can be summarized in a decision table, as depicted in Table 1.  
The results of the particular surveys can be mapped as follows:  
\[x\Big{(}\mathcal{A}^{i},\;\mathcal{CC}\Big{)}=\sum_{k=1}^{l}w_{k}^{i}s_{k}\]  
In order to compare different alternatives with respect to several criteria underlying different units, a value function for the criterion \(\mathcal{C}_{j}\) maps scores to a common scale, as follows:  
\[v_{j}=\left\{\begin{array}{c}\mathbb{R}\rightarrow[0,1]\\ x_{ij}\mapsto v_{j}\big{(}x_{ij}\big{)}\end{array},\;j=1,\ldots,n\right.\]  
Hence, the scores of all criteria for an alternative \(\mathcal{A}^{i}\) can be summarized in the vector  
\[v^{i}=(v_{1}(x_{i1}),\;\ldots,v_{n}(x_{in}))\]  
The overall score for the alternative \(\mathcal{A}^{i}\) is calculated according to  
\[v\Big{(}\mathcal{A}^{i}\Big{)}=\sigma\Big{(}v^{i},w\Big{)}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria (Units)/Alternatives** & \(\mathcal{C}_{1}\) **(Unit 1)** & \(\mathcal{C}_{2}\) **(Unit 2)** & \(\ldots\) & \(\mathcal{C}_{n}\) **(Unit m)** \\ \hline \(\mathcal{A}^{1}\) & \(x_{11}\) & \(x_{12}\) & \(\ldots\) & \(x_{1n}\) \\ \(\mathcal{A}^{2}\) & \(x_{21}\) & \(x_{22}\) & \(\ldots\) & \(x_{2n}\) \\ \(\ldots\) & & & & \\ \(\mathcal{A}^{m}\) & \(x_{m1}\) & \(x_{m2}\) & \(\ldots\) & \(x_{mn}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Decision table of MCDA.  
with \(w=(w_{1},\dots,\)\(w_{n})\), \(\sum\limits_{j=1}^{n}w_{j}=1\), and \(\sigma:\left[0,\ 1\right]^{2n}\rightarrow\left[0,\ 1\right]\), where \(w_{j}\) is the preference with respect to the criterion \(C_{j}\).  
The methodology is illustrated in the flowchart in Figure 1.