An agent-based model of community joining


Jeremy Foote
Northwestern University


Benjamin Mako Hill
University of Washington


Nate TeBlunthuis
University of Washington

How do we decide which groups to join?

Groups size distributions vary

Universities look like this:

Data from Wikidata

Online groups

While reddit looks like this:

Data from Stuck_in_the_Matrix on BigQuery

Why?

Preferential Attachment

  • One model proposed as source of long-tail distributions is preferential attachment (Barabási, 1999)
  • People probabilistically join groups based on their relative size

One small problem

  • It’s not realistic
    • Observed distributions often aren’t power-law (Broido and Clauset, 2018)
    • People don’t make decisions in this way

A better model

Expected value of joining

  • Resnick et al. (2011)
    • People estimate the benefits of joining
      • Participation benefits (information, friendship)
        • Based on estimate of future growth
      • Early adopter benefits (influence)
    • Estimate the costs (new technology, learning new norms, etc.)
    • Join if benefits exceed costs

A few problems

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

Is it reasonable?

Our agent-based model

  • Basic structure
    • Start with \(N\) potential contributors and \(X\) empty communities
  • Every “month”:
    • \(X\) new communities are created
    • \(n\) users are chosen at random
    • Each user is presented with a “choice set” of \(x\) communities
      • Choice sets are randomly chosen, weighted by community size
      • The user estimates the future size and joins the community with the greatest expected utility

Utility

Decision algorithms

  • Random
  • Biggest
  • Linear growth
  • Recent growth
  • Learning model

Learning model

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

Results

Empirical distributions

Simulated distributions

Limitations

Agent-based modeling

  • Better for disproving than proving
    • Other models could match just as well
  • Choices about where and how to simplify

Future work

  • Surveys and experiments
    • Do past experiences influence decisions?
    • What do actual “choice sets” look like?
  • Modeling interests explicitly
  • Explaining longitudinal patterns of participation

Conclusion

A more realistic model

  • 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
    • Likely due to heterogeneity in expectations

The End

Thanks!


Jeremy Foote
@jdfoote


Benjamin Mako Hill
@makoshark


Nate TeBlunthuis
@groceryheist

Appendix

Utility

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

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 size after 6 months

All models

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