3.1.2. The Degree of the Information Entropy

Information entropy *E<sup>l</sup>* (*p*) is calculated for each of the *pkl* elements and aggregated through the set of possible responses:

$$E\_l(p) = -\sum\_{k=1}^{K} p\_{kl} \log\_2(p\_{kl}).\tag{4}$$

Normalization of the *E<sup>l</sup>* (*p*) is performed dividing the *E<sup>l</sup>* (*p*) by the maximum entropy attainable over the *L* possible survey items. For every value *k* entropy is maximized when *p<sup>k</sup>* = <sup>1</sup> *K* . Therefore, the normalized entropy is calculated by Equation (5):

$$\widetilde{E}\_l(p) = -\frac{E\_l(p)}{\log\_2\left(\frac{1}{\widetilde{\mathbb{K}}}\right)}; l = 1, 2, \dots \\ \text{L. } 0 \le \widetilde{E}\_l(p) \le 1. \tag{5}$$
