Internet Communities’ Integration Index Hierarchical Model

Application of the hierarchy analysis method in system research

To assess the influence of parameters on the integration indicator, the hierarchy analysis method of Saaty (1980, 1987) is applied. There are many examples of the hierarchy analysis method successful application in various fields: historical multidisciplinary review (Ishizaka & Labib, 2011), project management in the engineering applications development (Aguilar-Lasserre et al., 2009; Ivanco et al., 2017; Nguyen et al., 2017; Lambert, 1991; Ho & Ma, 2017), the industrial mills research for multi-stage materials processing (Zhirov, 2011), analysis of the universities indicators (Kazancev, 2010), the applications evaluation for participation in competitions for the complex systems development (Perevedentcev, 2017), the highly qualified athletes ranking (Gorokhov, 2016), improving the enterprise efficiency (Blagodatskij, 2015).

Advancing a Minimal Hypothetical Model

To obtain an objective and reliable degree of Integration of the Internet community mobilization a set of minimum necessary parameters should be defines. These are sociocultural aspects, the group goals and values, the mobilization potential and internal communications volume. This analysis is based on the Pareto principle selection of parameters.

Defining variables for setting integration parameters

It is required to select variables for turning integration parameters from the set:

• Sociocultural aspects (ritualized practices) - the proportion of posts that use hashtags (#), the number of hashtags, their own language of communication, thematic fashion;

• Goals and values of the group - dominant strategies (exclusivity / leadership / struggle / survival, etc.), political orientation (opposition / pro-government / neutral), average share of material with links to foreign content (compliance with global sociocultural trends), average share of material with links to Russian content (compliance with national sociocultural trends), the degree of specificity of goals (narrowly practical, achievable, easily measurable / abstract, broad, poorly measurable);

• The volume of internal communications - the number of views of publications in the feed for the week, the number of posts in “discussions” for the week, the number of comments in the main feed for the week;

• Mobilization potential - the geographical spread / localization of actions, the number of effective external collective actions (per month (for self-assessment)), the availability of instructions on how to act in certain situations online (per month), the average number of participants in events offline (per month (for self-assessment)).

Representing Internet Community Integration as a Hierarchy

The desire of a social group to integrate is influenced by forces formed by the internal characteristics of the community, the dynamics of its indicators and external factors (Figure 01 ).

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Definition 1. (Hierarchical model of the indicator of integration of the Internet community) We will consider the characteristics of the Internet community as a hierarchical system. We distinguish many levels in the system, represented as:

$I=\left\{I_i\right\},i=\overline{\mathrm{1},m}$ (1)

We observe complex interactions with higher hierarchy levels at each hierarchy level. We apply the method of hierarchy analysis of Saaty (1980) to formalize the decision-making process to Internet community integration. Consider system levels I . The $I_{\mathrm{0}}$ level is the goal of the system, that integration in the online community.

Definition 2. (Level of influence of forces) At the first level of system I ₁, we distinguish the forces influencing the integration process in the online community as (2):

$W_{I_{\mathrm{1}}}=\left\{{W_{I_{\mathrm{1}}}}_j\right\},j=\stackrel{¯}{\mathrm{1},n_{I_{\mathrm{1}}}}$,(2)

As already noted, the forces are: the community itself ( ${W_{I_{\mathrm{1}}}}_{\mathrm{1}}$), community dynamics ( ${W_{I_{\mathrm{1}}}}_{\mathrm{2}}$), external factors ( ${W_{I_{\mathrm{1}}}}_{\mathrm{3}}$).

Definition 3. (Level of active elements of the system) The active elements (actors) that drive the forces put at the second level of system I ₂ (2):

$W_{I_{\mathrm{2}}}=\left\{{W_{I_{\mathrm{2}}}}_j\right\},j=\stackrel{¯}{\mathrm{1},n_{I_{\mathrm{2}}}}$, (2)

where ${W_{I_{\mathrm{2}}}}_{\mathrm{1}}$ – group age, ${W_{I_{\mathrm{2}}}}_{\mathrm{2}}$ – community volume dynamics, ${W_{I_{\mathrm{2}}}}_{\mathrm{3}}$ – quantitative composition of the core of the group, ${W_{I_{\mathrm{2}}}}_{\mathrm{4}}$ – mobilization potential, ${W_{I_{\mathrm{2}}}}_{\mathrm{5}}$ – modularity, ${W_{I_{\mathrm{2}}}}_{\mathrm{6}}$ – external communication volume, ${W_{I_{\mathrm{2}}}}_{\mathrm{7}}$ – internal communication volume, ${W_{I_{\mathrm{2}}}}_{\mathrm{8}}$ – community volume, ${W_{I_{\mathrm{2}}}}_{\mathrm{9}}$ – trust level, ${W_{I_{\mathrm{2}}}}_{\mathrm{10}}$ – cohesion level, ${W_{I_{\mathrm{2}}}}_{\mathrm{11}}$ – leadership features, ${W_{I_{\mathrm{2}}}}_{\mathrm{12}}$ – participants features, ${W_{I_{\mathrm{2}}}}_{\mathrm{13}}$ – publications subject features, ${W_{I_{\mathrm{2}}}}_{\mathrm{14}}$ – group goals and values, ${W_{I_{\mathrm{2}}}}_{\mathrm{15}}$ – online and offline activity features, ${W_{I_{\mathrm{2}}}}_{\mathrm{16}}$ – social network software and hardware features, ${W_{I_{\mathrm{2}}}}_{\mathrm{17}}$ – political and legal aspects, ${W_{I_{\mathrm{2}}}}_{\mathrm{18}}$ – financial aspects, ${W_{I_{\mathrm{2}}}}_{\mathrm{19}}$ – sociocultural aspects.

Definition 4. (Actors impact indicators level) At the third level, there are many indicators characterizing the actors that drive the forces that influence the Internet communities’ integration process. Highlight the level of indicators I ₃ and its elements (3):

$W_{I_{\mathrm{3}}}=\left\{{W_{I_{\mathrm{3}}}}_j\right\},j=\stackrel{¯}{\mathrm{1},n_{I_{\mathrm{3}}}}$.(3)

Hierarchy analysis method application to identify the Internet community elements weights

Set the influence of level’s I ₁ forces $I_{\mathrm{1}}\to I_{\mathrm{0}}$ to the system’s goal I ₀. First: weight the importance of the elements in pairs $W_{I_{\mathrm{1}}}=\left\{{W_{I_{\mathrm{1}}}}_j\right\},j=\stackrel{¯}{\mathrm{1},n_{I_{\mathrm{1}}}}$, where the dominance of the element ${W_{I_{\mathrm{1}}}}_k$ in relation to ${W_{I_{\mathrm{1}}}}_m$ is denoted by an integer from the relationship scale $a_{km}$. Second: get the matrix $A_{I_{\mathrm{1}}}=\left[a_{ij}\right]$ of pairwise comparisons and of $n_{I_{\mathrm{1}}}\times n_{I_{\mathrm{1}}}$dimensions is filled in after $C_{{\mathrm{}}_{n_{I_{\mathrm{1}}}}}^{\mathrm{2}}$ comparisons.

It is necessary to answer the question about the integration coefficient's relevance for filling the matrix $A_{I_{\mathrm{1}}}$ using the elements of I ₁ levels, that we take in pairs. Level I ₁ consists of 3 elements: the community itself ( ${W_{I_{\mathrm{1}}}}_{\mathrm{1}}$), community dynamics ( ${W_{I_{\mathrm{1}}}}_{\mathrm{2}}$), external factors ( ${W_{I_{\mathrm{1}}}}_{\mathrm{3}}$). The comparisons are presented in Table 01 .

Fill the matrix $A_{I_{\mathrm{1}}}$, taking according to Saaty that comparing the effect ${W_{I_{\mathrm{1}}}}_k$ to I ₀ towards to ${W_{I_{\mathrm{1}}}}_m$ is inverse influence ${W_{I_{\mathrm{1}}}}_m$ to I ₀ towards to ${W_{I_{\mathrm{1}}}}_k$: $a_{mk}=\frac{\mathrm{1}}{a_{km}}$. Note that the element comparison with itself $a_{kk}=\mathrm{1}$ shows equal importance. The system’s goal forces influence pairwise comparison shown in Table 02 .

The result of solving equation (4) is right eigenvector ${\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}$ of matrix $A_{I_{\mathrm{1}}}$, corresponding to the maximum eigenvalue:

$A_{I_{\mathrm{1}}}{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}={\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}{I}_{\mathrm{1}}}{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}$(4)

Maximum eigenvalue vector can be found through an iterative procedure (Kalitkin, 1990):

• Let $y^{\left(\mathrm{0}\right)}=\{\mathrm{1},...,\mathrm{1}\}$ unit vector of $n_{I_{\mathrm{1}}}$ dimension.

• Run the iterative process $y^{\left(k\right)}=A_{I_{\mathrm{1}}}{y}^{(k-\mathrm{1})}=A_{I_{\mathrm{1}}}^{k-\mathrm{1}}{y}^{\left(\mathrm{0}\right)}$ before reaching (5)

${\epsilon }^{\left(k\right)}=\left|\frac{y_j^{\left(k\right)}}{y_j^{(k-\mathrm{1})}}-\frac{y_j^{(k-\mathrm{1})}}{y_j^{(k-\mathrm{2})}}\right|\le \epsilon$ _,(5)

where $\epsilon$ is the calculation error ${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}{I}_{\mathrm{1}}}=\frac{y_j^{\left(k\right)}}{y_j^{(k-\mathrm{1})}}$.

The vector obtained at the last step of the iterative process $y^{\left(k\right)}$ is the solution to the equation $A_{I_{\mathrm{1}}}{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}={\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}{I}_{\mathrm{1}}}{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}$.

We get the vector (6) after vector’s coordinates normalizing ${\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}}$:

${\omega }_{I_{\mathrm{1}}}=\left\{\frac{{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}i}}{\underset{j=\mathrm{1}}{\overset{n_{I_{\mathrm{1}}}}{\sum }}{\omega \mathrm{\text{'}}}_{I_{\mathrm{1}}j}}\right\},i=\stackrel{¯}{\mathrm{1},n_{I_{\mathrm{1}}}}$,(6)

where ${\omega }_{I_{\mathrm{1}}}$ is vector of influence $I_{\mathrm{1}}$ to $I_{\mathrm{0}}$.

We obtain influence of forces on the goal of the system ${\omega }_{I_{\mathrm{1}}}$= (1/3;1/3;1/3). Integration processes is equal influenced by the Forces (Table 3 ).

$$CR=\mathrm{0,05}<\mathrm{0,1}$$

As a measure of correctness of judgment, the relation of consistency is introduced ( CR ) is the consistency index ratio ( CI ) of pairwise matrix $A_{I_j}$ to random index ( RI ) CR=CI/RI . RI is a CI to square matrix of n×n dimension filled by random numbers. For n×n matrixes CI is calculated by formula $CI=\frac{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}-n}{n-\mathrm{1}}$. $CR\le \mathrm{0,1}$ considered valid for matching matrix paired comparisons.

Carrying out similar calculations, we obtain all vectors ${\omega }_{I_j},j=\overline{\mathrm{1,4}}$ level elements influence $I_j\to I_{j-\mathrm{1}}$ through entire hierarchy $I$.

Evaluation matrix forming

The hierarchy of levels in a downward process is then considered. Starting from level I ₂ and considering the influence of its elements on a higher level (Table 04 ).

According to Table 04 , a matrix of pairwise comparisons in constructed (Table 05 ).

$$CR\approx \mathrm{0,13}<\mathrm{0,2}$$

The remaining matrices of level I ₂ are formed according to the procedure given above.

Priority vectors for evaluation matrices

We write priority vectors ${\omega }_{I_{\mathrm{2}}i},i=\overline{\mathrm{1},..\left|I_{\mathrm{1}}\right|}$ for evaluation matrix ${{\mathrm{А}}_{I_{\mathrm{2}}}}_i,i=\overline{\mathrm{1},..\left|I_{\mathrm{1}}\right|}$ I ₂ level in a form of matrix $W_{I_{\mathrm{2}}}=\left\{{\omega }_{I_{\mathrm{2}}i}\right\},i=\overline{\mathrm{1},..\left|I_{\mathrm{1}}\right|}$ , where $\left|I_{\mathrm{1}}\right|$is the cardinality of I ₁ (Table 08 ).

We now turn to the level of I ₃ (actors’ characteristics level). We consider its influence on the elements of the level I ₂.

We form matrices of paired comparisons similarly to the previous level (the results obtained for the characteristics of the community are given in Table 09 ).

A graphical representation of the results of calculations on the influence of actors on the integration process is shown in Figure 02 (Table 08 column “Community itself”). Also, according to Tables 08 and 09 , similar histograms of the distribution of the influence of variables are constructed.

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In figure 2 along the abscissa axis: 1 - the age of the group, 2 - the community dynamics volume, 3 - the group’s core quantitative composition, 4 - potential of mobilization, 5 - modularity, 6 - the volume of external communications, 7 - the volume of internal communications, 8 - the community volume, 9 – trust level, 10 - cohesion level.

The nomination of a minimal hypothetical model

The results can be used to advance the minimum in composition (necessary), hypothetical model of "integration of mobilization in online communities." By using the Pareto principle, the minimum set of Internet community's mobilization integration objective and reliable degree parameters (in decreasing order of importance): social and cultural aspects, values and goals of the group, the internal communications and volume of potential of mobilization.

Variables by which the listed parameters are fixed

Variables by which the listed parameters are fixed (Table 09 ):

• sociocultural aspects (ritualized practices);

• group goals and values;

• internal communication volume;

• mobilization potential.