This is the first post in a series where I discuss — in accessible terms — formal models that explain how status is produced, consolidated, and transmitted in social interaction. The starting point is a paper published in the American Journal of Sociology in 1996: “Status and Participation in Task Groups: A Dynamic Network Model”, by John Skvoretz and Thomas J. Fararo.
The Question
Imagine a jury deliberating, a faculty committee discussing parking policy, or a group of neighbors debating a drainage problem. Everyone arrives with different external statuses — rank, gender, ethnicity — but what happens inside the group is not fully determined by those prior differences.
How does an internal order ultimately emerge? Who speaks more? Whom does everyone listen to? Can someone with low external status end up dominating the discussion?
These questions motivate the Skvoretz and Fararo model.
Three Traditions the Paper Synthesizes
The model does not appear out of nowhere. It is a synthesis of three prior lines of research, each with its own logic:
1. Expectation States Theory (Berger, Cohen & Zelditch, 1966)
This tradition starts from an empirical observation: when group members differ on some diffuse status characteristic — gender, race, educational level — that activates expectations about who is more competent at solving the group’s task.
The central concept is the aggregate expectation state: each actor accumulates a value reflecting how much the group expects them to contribute. That value determines how much they participate, how much influence they exert, and how readily others accept their proposals.
The limitation of this tradition, through the mid-1990s, was that its models were static: they described the final distribution of participation but not the process by which that distribution emerges act by act.
2. Log-linear Participation Model (Balkwell, 1995)
Balkwell proposes a concrete mathematical function that translates expectation states into probabilities of directed participation — that is, not only how much each person speaks, but to whom they speak.
The empirical regularity it captures is elegant: if i outranks j in status, then j directs more acts to i than i directs to j. Those with higher status receive more participation from lower-ranked members and direct their own participation upward or toward equals.
\[E(a_{ij}) = \exp(\alpha + \gamma_i + \delta\gamma_j), \quad \delta > 1\]
Skvoretz and Fararo embed this function directly into their dynamic model.
3. E-state Structuralism (Fararo & Skvoretz, 1986)
This is the most important architectural piece. The idea is that actors develop relational orientations — called E-states — toward other actors that are not directly observable but that determine behavior.
Originally developed to explain the formation of dominance hierarchies in animal groups (using data on chickens), the logic is as follows:
- The state of the network — who has precedence over whom — constrains the events that can occur in interaction.
- Interaction events, in turn, stochastically generate new ties in the network.
- The process is a Markov chain that may or may not converge to a completely transitive hierarchy.
What Skvoretz and Fararo do in 1996 is reconfigure this framework for human discussion groups, incorporating the two prior traditions.
The Model in Plain Terms
The Central Concept: Precedence Tie
The basic unit of the model is the precedence tie: if xPy, the group recognizes — implicitly, without anyone declaring it — that x has more internal status than y. Think of it as an invisible arrow: x → y.
That arrow can arise from two sources:
- External status: x is a full professor, y is an assistant professor. The rank difference automatically activates precedence.
- Emergent behavior: x spoke first and with authority. The group interpreted this as a signal of competence, and the arrow formed.
The Five Axioms
The model is stated in five axioms that specify how the precedence network evolves act by act.
| Axiom | Name | What it says |
|---|---|---|
| 1 | Initial state | At the outset, no ties exist. Clean slate. |
| 2 | Stability | Once a tie forms, it does not dissolve. |
| 3 | Interactant effect | When x addresses y, xPy may form with a probability that depends on their external statuses. |
| 4 | Bystander effect | When z observes x address y, z may also update its ties with x and y. |
| 5 | Behavior | The probability that x speaks next depends on their accumulated internal status. |
Axiom 4 is the most important and the most counterintuitive. Each speech act can generate up to 8 precedence ties via bystanders, versus only 1 via the direct interactant effect. Hierarchies are consolidated primarily through those who watch, not those who speak.
The Parameters
The model has three main parameters:
- η (eta): probability that the external status characteristic is activated in a given act.
- π (pi): probability that a tie forms through behavioral interpretation (when external status is not activated).
- θ = ρ·π (theta): probability of the bystander effect. By definition, θ ≤ π.
The Simulation: Act by Act
The process can be visualized concretely. Skvoretz and Fararo use the example of a 6-person committee — 3 full professors (high status) and 3 assistant professors (low status) — discussing campus parking policy.
In the widget below you can follow the process act by act. Each click represents one speech act. Notice how the arrows form, and pay particular attention to how bystanders (those who only observe) generate the majority of ties.
⬤ Blue = high status (H1–H3, full professors) | ○ Gray = low status (L1–L3, assistant professors) | → Orange = new tie
The result in this example is striking: in just 9 speech acts, the 6-person group forms all 15 precedence ties needed for a complete status order. And 14 of those 15 ties emerged via bystander effects, not via the direct interactant effect.
What Does the Model Predict?
The simulation (100 runs per parameter combination) allows us to answer four concrete questions:
1. How long does it take the group to stabilize? It depends primarily on the bystander effect (θ). The larger θ, the fewer acts are needed before all pairs have a tie. Mixed-status groups converge faster than homogeneous ones.
2. How often does a fully transitive hierarchy emerge? Not always — and that matters. Complete transitivity is contingent, not guaranteed. It depends on the bystander effect being strong enough. This directly challenges the assumption of Fisek et al. (1991), who treated transitive hierarchies as the default outcome.
3. How much does speaking early matter? Quite a bit, especially when η and π take intermediate values. Whoever takes the floor early can capture precedence ties that then feed back into their future participation.
4. Can someone with low external status end up on top? Yes, under specific conditions — when η is low (external status is not easily activated) and π is high (behaviors are readily interpreted as status claims). This gives the model a more realistic prediction profile than its predecessors.
Why This Paper Matters
Skvoretz and Fararo accomplish something few sociological models manage: linking the social psychology of small groups with network analysis in a formal model that is simultaneously mathematically rigorous and substantively interpretable.
The bystander mechanism — that hierarchies are consolidated primarily through those who observe, not those who speak — is a lasting theoretical contribution. It suggests that status is not something negotiated bilaterally but something that emerges from the collective dynamics of observation and interpretation.
For researchers working on social mobility, labor markets, or interaction networks, this paper offers a precise formal vocabulary for thinking about how hierarchical positions form, consolidate, and — under specific conditions — can be subverted.
References
Skvoretz, J., & Fararo, T. J. (1996). Status and participation in task groups: A dynamic network model. American Journal of Sociology, 101(5), 1366–1414.
Fararo, T. J., & Skvoretz, J. (1986). E-state structuralism: A theoretical method. American Sociological Review, 51(4), 591–602.
Balkwell, J. W. (1995). Status. In K. S. Cook, G. A. Fine, & J. S. House (Eds.), Sociological Perspectives on Social Psychology. Allyn and Bacon.
Fisek, M. H., Berger, J., & Norman, R. Z. (1991). Participation in heterogeneous and homogeneous groups: A theoretical integration. American Journal of Sociology, 97(1), 114–142.
Berger, J., Cohen, B. P., & Zelditch, M. (1966). Status characteristics and expectation states. In J. Berger & M. Zelditch (Eds.), Sociological Theories in Progress, Vol. 1. Houghton Mifflin.