Analysis and Modeling of Activity-Selection Behavior in Collaborative Knowledge-Building

Abstract

People neither behave uniformly in their social lives nor is their behavior entirely arbitrary. Rather, their behavior depends on various factors such as their skills, motives, and backgrounds. Our analysis shows that such a behavior also prevails in the websites of Stack Exchange. We collect and analyze the data of over 5.3 million users from 156 Stack Exchange websites. In these websites, users’ diverse behavior shows up in the form of different activities that they choose to perform as well as how they stimulate each other for more contribution. Using the insights gained from the empirical analysis as well as the classical cognitive theories, we build a general cognitive model depicting the users’ interaction behavior emerging in collaborative knowledge-building setups. Further, the analysis of the model indicates that for any given collaborative system, there is an optimal distribution of users across its activities that leads to the maximum knowledge generation. We also apply the model on Stack Exchange websites and identify the under-represented activities.

A Appendix

1.1 A.1 Stack Exchange Data Set Statistics

Table 2. Data Set Statistics (The websites are sorted as per their creation time)

1.2 A.2 Stack Exchange Policies Regarding Commenting and Editing

As per StackExchange rules, users require at least 50 reputation points to be able to unlock the feature of commenting on questions and answers that they don’t own. This policy has indeed been laid in order to discourage spam comments by casual users as well as to emphasize that Stackexchange restricts itself to a Q&A portal rather than a discussion forum such as ‘ubuntuforums.org’ where even comments such as ‘Thanks, that was useful’, ‘I agree’, ‘I have the same problem’ are allowed as answers. Moreover, commenting is done to better understand a question or an answer. It basically adds a small discussion thread along with a question or an answer, which Stack Exchange community discourages. However, one may ask the reason for having encountered some number of Uni-C in commenting in such a scenario. The reason for that are two more StackExchange policies, whereby if a user gets 200 reputation points on any one Stack Exchange site, then that user automatically gets an association bonus of 100 on every site, enabling him to contribute across any activity on any of the StackExchange websites. Also, StackExchange automatically converts trivial answers containing a link to another question in the network to comments on the question. Due to these reasons, we could find some, although small, number of Uni-C in commenting. On the other hand, the reason for having less number of Uni-C in editing is supposed to be the requirement that until a user gathers 2000 reputation points, their edits are likely to be rejected, i.e. they can not actually edit the content; they can only suggest the edits. Additionally, there is an upper limit of the reputation points that can be gained by editing others’ content viz. 1000 points. Beyond this, a user can not earn more reputation by editing. This further discourages the users to become an Uni-C in editing.

1.3 A.3 Uni-C, Bi-C and Tri-C in Stack Exchange Websites

Table 3. Percentage of Uni-C, Bi-C and Tri-C across websites. (The websites are sorted as per their creation time.)

1.4 A.4 Proportion of Uni-C Across the Activities in Stack Exchange Websites

Table 4. Percentage of Uni-C across the activities. (The websites are sorted as per their creation time.)

It should be noted that as per StackExchange policies, users require atleast 15 reputation points to be able to vote. The reason for the presence of uni-C in voting is the association bonus⁵, whereby users who have atleast 200 reputation points on any of the StackExchange websites, get a bonus of 100 on each new StackExchange website that they register, in addition to the 1 reputation point that they normally get upon registering. This leads to a total of 101 reputation points automatically provided to them, enabling them to upvote or downvote content on the new website despite no contribution in questioning or answering on these new websites.

Further, the presence of less than 1% (i.e., 0.34%) uni-C in voting on StackOverflow depicts the possibility of users gaining bonus reputation points on other websites due to their contribution on StackOverflow rather than the other way around, as it is the oldest website.

1.5 A.5 Method Used for Finding the Optimal k

To verify the optimal value of k, we use a method provided by He et al. [24]. In their method, the authors compute two parameters ‘Cluster compactness (CMP)’ and ‘Cluster separation (SEP)’, where CMP captures the intra-cluster distances and SEP captures the inter-cluster distances. The formulae for CMP and SEP are given as below:

Cluster Compactness (CMP):

$$CMP = \frac{1}{C}\sum _{i}^{C}{\frac{v(c_i)}{v(X)}}$$

where,

$$v(X) = \sqrt{{\frac{1}{N}}\sum _{i=1}^{N}d^2(x_i, \bar{x})}$$

Cluster Separation (SEP):

$$SEP = \frac{1}{C(C-1)}\sum _{i=1}^{C}\sum _{j=1, j\ne i}^{C}\exp \left( {-\frac{d^2({x_c}_i, {x_c}_j)}{2\sigma ^2}}\right) $$

The formula for SEP is such that a smaller value of SEP indicates a larger inter-cluster distance. Further, the clusters should also be compact (measured by CMP). Therefore, for the optimal value of k, the values of both CMP, as well as SEP, should be minimum. The authors suggest using another parameter OCQ (Overall Cluster Quality) which is given as:

$$OCQ(\alpha ) = \alpha * CMP + (1 - \alpha ) * SEP$$

where $\alpha$ indicates the relative weight assigned to inter-cluster and intra-cluster distances and lies between 0 and 1. A value of 1/2 for $\alpha$ indicates equal weight for both CMP and SEP. For our analysis, we considered $\alpha$ to be 1/2.

We used this method to compute the optimal k for all the websites. The Table in Fig. 5 shows the value of k along with the number of websites for which that value of k was found optimal. For most of the websites, k = 3 was the optimal value of k.

Table 5. Number of websites with the given ideal k. For 73.71% of the websites, ideal k value was found to be 3.

1.6 A.6 User-Distribution Obtained For Stack Exchange Websites

Table 6. Percentage Distribution of questioners, answerers and voters for each website.

1.7 A.7 Model Parameters for the Systems Studied in Chapter 3

The values in the matrix T were chosen uniformly at random between 0.00007 and 0.005 making sure that $\rho (NT) < 1$.

System 1: n = 100, $K_c(\infty )$ = 14289.74, $\mathcal {D}$ = (22, 35, 43)

$$ T = \left[ {\begin{array}{ccc} 0.00045596 &{} 0.00435622 &{}0.00287159\\ 0.00382782 &{} 0.00076362 &{} 0.00499575\\ 0.00399529&{} 0.00348565 &{} 0.0018039\\ \end{array}}\right] $$

System 2: n = 100, $K_c(\infty )$ = 13331.63, $\mathcal {D}$ = (19, 51, 30)

$$ T = \left[ {\begin{array}{ccc} 0.00078797 &{} 0.00359952 &{} 0.00363374 \\ 0.00194002 &{} 0.0018636 &{} 0.00456399 \\ 0.0026924 &{} 0.00233821 &{} 0.00057316 \\ \end{array}}\right] $$

System 3: n = 200, $K_c(\infty )$ = 46239.11, $\mathcal {D}$ = (64.5, 18.5, 17)

$$ T = \left[ {\begin{array}{ccc} 0.00257957 &{} 0.00330136 &{} 0.00199484 \\ 0.0033283 &{} 0.00098843 &{} 0.00397102\\ 0.00491812 &{} 0.0016636 &{} 0.00101264\\ \end{array}}\right] $$

System 4: n = 200, $K_c(\infty )$ = 37732.05, $\mathcal {D}$ = (44, 44, 12)

$$ T = \left[ {\begin{array}{ccc} 0.00025509 &{} 0.00491508 &{} 0.00236663\\ 0.00365481 &{} 0.00047938 &{} 0.00425228\\ 0.0033825 &{} 0.0004316 &{} 0.00066393\\ \end{array}}\right] $$

Systems with Self-triggering = 0: n = 100 in all three systems.

System 1: $K_c(\infty )$ = 12536.23, $\mathcal {D}$ = (38, 32, 30)

$$ T = \left[ {\begin{array}{ccc} 0. &{} 0.00265766 &{} 0.00448791 \\ 0.00400489 &{} 0. &{} 0.00111834\\ 0.00194009 &{} 0.00390131 &{} 0. \\ \end{array}}\right] $$

System 2: $K_c(\infty )$ = 11114.29, $\mathcal {D}$ = (39, 37, 24)

$$ T = \left[ {\begin{array}{ccc} 0. &{} 0.00299839 &{} 0.00122855\\ 0.00070994 &{} 0. &{} 0.00168737\\ 0.00149221 &{} 0.00082065 &{} 0. \\ \end{array}}\right] $$

System 3: $K_c(\infty )$ = 11924.27, $\mathcal {D}$ = (34, 28, 38)

$$ T = \left[ {\begin{array}{ccc} 0. &{} 0.00264557 &{} 0.00119586\\ 0.00115856 &{} 0. &{} 0.00398131\\ 0.00448212 &{} 0.00097011 &{} 0. \\ \end{array}}\right] $$