Agent-based model of community joining

An agent-based model of community joining

Jeremy Foote
Northwestern University

Benjamin Mako Hill
University of Washington

Nate TeBlunthuis
University of Washington

<!-- ## An obvious(?) proposition

The sizes of groups are determined by who joins them. -->

## How do we decide which groups to join?

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### Groups size distributions vary

ICA groups look like this:

<aside class="notes">Different constraints lead to different distributions. This is the distribution of members per ICA division/interest group</aside>

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### Online groups

While reddit looks like this:

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# Why?

<aside class = 'notes'>So, whence these skewed distributions? There have been a number of explanations suggested...</aside>

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### Preferential Attachment

* One model proposed as source of long-tail distributions is <span class="highlight">preferential attachment</span> (Barabási, 1999) 
* People probabilistically join groups based on their relative size

<aside class='notes'>One of the most popular is a model called 'preferential attachment'. According to this model, people survey the landscape of possible communities
to join, and probablistically choose between them based on their current relative size</aside>

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### One small problem

* It's not realistic 
	* People don't make decisions in this way

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### More realistic model

* Resnick et al. (2011)  
  * People estimate the benefits of joining 
  <ul>
    <li class = 'fragment'><span class="highlight">Participation benefits</span> (information, friendship) </li>
    <ul>
	  <li class='fragment'> Based on estimate of future growth </li>
	</ul>
    <li class = 'fragment'><span class="highlight">Early adopter benefits</span> (influence) </li>
    </ul>
  <li class = 'fragment'>Estimate the <span class="highlight">costs</span> (new technology, learning new norms, etc.) </li>
  * Join if benefits exceed costs

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### A few problems

* Only applies to single decision 
* Doesn't explain how people estimate future growth  
* Not derived from empirical data

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### Agent-based modeling

* Basic structure:
  * Start with $N$ potential contributors
  * Every "month" $X$ new communities are created
    * $n$ users are chosen at random
    * Each user is presented with a "choice set" of $x$ communities
	    * These choice sets are randomly chosen, weighted by community size
    * The user estimates the future size and joins the community with the greatest utility

<aside class = "notes"> 
Astute audience members will recognize that this is similar to the models of preferential attachment that I criticized earlier in the talk. One key difference is that this
doesn't assume that individuals choose communities based on popularity. Rather, the communities they perceive are influenced by popularity. This could represent,
for example, communities featured on a site's homepage.
</aside>

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#### Utility

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### Decision algorithms

* <span class='highlight'>Random</span>
* Biggest
* <span class = 'highlight'>Linear growth</span>
* Recent growth
* <span class='highlight'>Learning model</span>

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### Learning model

* Agents fit a regression model on previously joined communities
* They then predict the growth of their current choice set

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## Results

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## Discussion

* We don't need preferential attachment  
* A Resnick et al. model can produce realistic distributions  
	* But  it's very sensitive to how people make estimates  
	* Only learning models produced realistic outcomes  
		* Possibly due to heterogeneity in expectations

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## Lessons from our approach

* ABM allowed us to: 
  * Cross the micro/macro divide 
  * Explore the unmeasurable 
  * Compare different theories 
    * Better for disproving than proving 
  * Explore different assumptions  
    * Need to define everything   
    * Difficult to find the right level of complexity  
		
<aside class = "notes">Can't take anything about the process for granted, everything has to be defined.
		The problem is not that you have to make assumptions explicit, but that you have to make everything explicit.
		In observation, many things are taken for granted.
		
		A related problem is that it's difficult to decide where to add complexity. In our model, communities are identical and agents are identical. It would make the model more realistic to add heterogeneity in the interests of users, but makes it harder to analyze the effect of choice algorithms.
</aside>

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<h4>
           Thanks!
          </h4>
              <div class="container">
                <div class="col">
                  <img src="images/jeremy.jpg" height="139px"/><br/>
                  Jeremy Foote<br/>
                  <small>
                  @jdfoote
                  </small>
                </div>
                <div class="col">
                  <img src="images/mako.jpg" height="139px"/><br/>
                  Benjamin Mako Hill<br/>
                  <small>
                  @makoshark
                  </small>
                </div>
                <div class="col">
                  <img src="images/nate.jpg" height="139px"/><br/>
                  Nate TeBlunthuis<br/>
                  <small>
                  @groceryheist
                  </small>
                </div>
              </div>
              </div>

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# Appendix

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### Utility

* Participation benefits (PB)
	* $PB = log(S + 1)$
* Early adopter benefits (EA)
	* $EA = log(S + 1)/log(i + 1)$
* Cost = $X$
* $U = PB + EA - C$

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# Learning model:

\begin{align}
log(growth) &=\beta_0 + \beta_1 \times S_j + \beta_2 \times A_j \\\
&+  \beta_3  \times (A_c - A_j) + \beta_4 \times S_c
\end{align}

* $S_c$ = current size, $A_j$ = age when joined
* Predicted growth after 6 months

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# All models